A power assignment over parallel Gaussian broadcast channels splits a power budget at the access point among all channel-user pairs subject to per-channel upper-bounds on the sum-power, and yields a rate allocation to all channel-user pairs. Its weighted energy efficiency (WEE) is the ratio of its weighted sum-rate over its sum-power plus a fixed positive overhead. The problem Max-WEE seeks a power assignment maximizing the WEE. Special variants of Max-WEE with unit weights or two users per channel have been extensively studied in the literature. But none of the existing algorithms for those special variants have known bounds on running time, mainly because they follow the general-purposed methods for fractional programming. In this paper, we first derive fundamental properties and closed-form expressions of maximum WEE. Then we devise a simple water-filling algorithm for Max-WEE. Assuming all users are presorted by weight, the water-filling algorithm haslinearcomplexity in the number of channel-user pairs. Under a mild presorting condition, we further develop alinear-complexity algorithm for Max-WEE subject to rate demand.

A power assignment over Gaussian broadcast channels splits the power budget at the access point among all user-channel pairs subject to per-channel upper-bounds on the sum-power, and is optimal if it maximizes the weighted sum-rate (WSR). In this paper we first present a geometric algorithm for computing an optimal power assignment over single Gaussian broadcast channel, which has linear complexity if all users are presorted either by weight or by noise. We also provide an intuitively appealing water-filling interpretation of this geometric algorithm. By leveraging such water-filling interpretation, we develop a water-filling algorithm for computing an optimal power assignment over parallel Gaussian broadcast channels, whose complexity is linear in the number of user-channel pairs if all users are presorted by weight. From these algorithmic studies, we derive clean and simple expressions of the maximum WSR in both integral forms and sum forms. By exploiting the rich property of those forms, we further give a linear-complexity algorithm for computing a power budget at the access point, subject to a given upper bound, which maximizes the difference between the maximum WSR and a linear cost of the power budget. The algorithmic studies in this paper also reveal that a single Gaussian broadcast channel can be decomposed into parallel Gaussian single-user channels which preserve the maximum WSR.

Major cloud service providers with well-equipped infrastructure, experienced machine learning (ML) expertise, and enriched training datasets are building ML-as-a-Service (MLaaS) systems, in which clients can query ML-based prediction services with their data. Instead of moving private data to the cloud, in this work, we design, implement, and evaluate a novel secure ML system to enable MLaaS on edge devices. To protect the proprietary ML models on edge devices from revealing to the clients while maintaining a real-time inference is challenging. Existing privacy-preserving ML techniques can hardly satisfy real-time requirements. In our solution, we employ a secure enclave (e.g., SGX) to offer security and provide better efficiency than cryptographic techniques. However, the enclave alone cannot achieve real-time capability due to its limited capacity. We observe that the ML model imposes a severe accuracy degradation when adding noise to a few model weights. Based on this, we design a suite of novel solutions to optimize the performance of secure enclave-based inference service at the edge by enclosing only$1\%$computation within secure enclaves. Our work can achieve up to a$7.8\times$increase in efficiency and a$27\times$reduction in memory usage compared to the state-of-the-art.

Hackers on the Internet usually send attacking packets using compromised hosts, called stepping‐stones, in order to avoid being detected and caught. With stepping‐stone attacks, an intruder remotely logins these stepping‐stones using programs like SSH or telnet, uses a chain of Internet hosts as relay machines, and then sends the attacking packets. A great number of detection approaches have been developed for stepping‐stone intrusion (SSI) in the literature. Many of these existing detection methods worked effectively only when session manipulation by intruders is not present. When the session is manipulated by attackers, there are few known effective detection methods for SSI. It is important to know whether a detection algorithm for SSI is resistant on session manipulation by attackers. For session manipulation with chaff perturbation, software tools such as Scapy can be used to inject meaningless packets into a data stream. However, to the best of our knowledge, there are no existing effective tools or efficient algorithms to produce time‐jittered network traffic that can be used to test whether an SSI detection method is resistant on intruders’ time‐jittering manipulation. In this paper, we propose a framework to test resistency of detection algorithms for SSI on time‐jittering manipulation. Our proposed framework can be used to test whether an existing or new SSI detection method is resistant on session manipulation by intruders with time‐jittering.

Intruders on the Internet usually launch network attacks through compromised hosts, called stepping stones, in order to reduce the chance of being detected. With stepping‐stone intrusions, an attacker uses tools such as SSH to log in several compromised hosts remotely and create an interactive connection chain and then sends attacking packets to a target system. An effective method to detect such an intrusion is to estimate the length of a connection chain. In this paper, we develop an efficient algorithm to detect stepping‐stone intrusion by mining network traffic using the k‐means clustering. Existing approaches for connection‐chain‐based stepping‐stone intrusion detection either are not effective or require a large number of TCP packets to be captured and processed and, thus, are not efficient. Our proposed detection algorithm can accurately determine the length of a connection chain without requiring a large number of TCP packets being captured and processed, so it is more efficient. Our proposed detection algorithm is also easier to implement than all existing approaches for stepping‐stone intrusion detection. The effectiveness, correctness, and efficiency of our proposed detection algorithm are verified through well‐designed network experiments.

Attackers on the Internet often launch network intrusions through compromised hosts, called stepping-stones, in order to reduce the chance of being detected. In a stepping-stone attack, an attacker uses a chain of hosts on the Internet as relay machines and remotely login these hosts using tools such as SSH. An effective method to detect stepping-stone intrusion is to estimate the length of a connection chain. In this paper, we develop an efficient algorithm to detect stepping-stone intrusion by mining network traffic using the k-Means clustering algorithm. Our proposed detection algorithm does not require a large number of TCP packets to be captured and processed. The length of a connection chain can be accurately determined by using our proposed detection method. Our proposed detection algorithm is more efficient and easier to implement than all of the existing connection-chain based approaches for stepping-stone intrusion detection. The effectiveness and correctness of our proposed detection algorithm are verified through well-designed network experiments.

Microgrids equipped with renewable energy resources have proven to be critical building blocks on the power grid that can greatly improve the grid performance. A promising application would be enabling microgrids to utilize their local energy for further balancing the regional supply and demand at different times - ensuring better system economics and reliability. However, due to the privacy concerns on continuously revealing each microgrid's local data for deriving real-time optimal balancing decisions, the application of such promising cooperative technique is still limited. In this paper, we design an efficient cryptographic protocol for privately balancing the regional supply and demand, as well as each microgrid's local supply and demand in real time. We prove the security of our protocol against both passive and active adversaries. Meanwhile, we implemented a prototype of the Pairing system that integrates cryptographic protocol and the power transmission network. We mount the real smart grid datasets into Pairing in real time for system evaluations. The experimental results demonstrate the practicality of our system by scaling to hundreds of microgrids with high accuracy and efficient system performance.

Utilizing the intelligence at the network edge, edge computing paradigm emerges to provide time-sensitive computing services for Internet of Things. In this paper, we investigate sustainable computation offloading in an edge-computing system that consists of energy harvesting-enabled mobile devices (MDs) and a dispatcher. The dispatcher collects computation tasks generated by IoT devices with limited computation power, and offloads them to resourceful MDs in exchange for rewards. We propose an online Rewards-optimal Auction (RoA) to optimize the long-term sum-of-rewards for processing offloaded tasks, meanwhile adapting to the highly dynamic energy harvesting (EH) process and computation task arrivals. RoA is designed based on Lyapunov optimization and Vickrey-Clarke-Groves auction, the operation of which does not require a prior knowledge of the energy harvesting, task arrivals, or wireless channel statistics. Our analytical results confirm the optimality of tasks assignment. Furthermore, simulation results validate the analytical analysis, and verify the efficacy of the proposed RoA.

Due to the merit without requiring charging cable, wireless power transfer technology has drawn rising attention as a new method to replenish energy for Wireless Rechargeable Sensor Networks. In this article, we study the mobile charger scheduling problem for multi-node recharging with deadline constraints. Our target is to maximize the overall effective charging utility and minimize the traveling time for moving as well. Instead of charging only once over a scheduling cycle, we incorporate the multi-node charging strategy with deadline constraints, where charging spots and tour are jointly optimized. Specifically, we formulate the effective charging utility maximization problem as a monotone submodular function optimization subject to a partition matroid constraint, and we propose a simple but effective ½-approximation greedy algorithm. After that, we derive the result of global scheduling and present the grid-based skip-substitute operation to further save the traveling time, which can increase the charging utility. Finally, we conduct the evaluation for the performance of our scheduling scheme. The simulation and field experiment results show that our algorithm excels in terms of effective charging utility.

Motivated by the fair rate allocation in a multiaccess Gaussian channel, this paper studies the problem of fair rate allocation over a generalized symmetric polymatroid with box constraints. The best-known algorithm for this problem has time complexity O(n5lnO(1)n). In this paper, we present a divide-and-conquer algorithm for this problem with quadratic running time. It is an implementation of a refined decomposing method for the more general separate concave maximization over a polymatroid with box constraints. A key ingredient of the algorithm is a linear-time algorithm for a generalized knapsack problem.

The rate capacity region of an uplink Gaussian channel is a generalized symmetric polymatroid. Practical applications impose additional lower and upper bounds on the rate allocations, which are represented by box constraints. A fundamental scheduling problem over an uplink Gaussian channel is to seek a rate allocation maximizing the weighted sum-rate (MWSR) subject to the box constraints. The best-known algorithm for this problem has time complexity O (n5 lnO(1) n). In this paper, we take a polymatroidal approach to developing a quadratic-time greedy algorithm and a linearithmic-time divide-and-conquer algorithm. A key ingredient of these two algorithms is a linear-time algorithm for minimizing the difference between a generalized symmetric rank function and a modular function after a linearithmic-time ordering.

Minimum-Latency Aggregation Scheduling (MLAS) has been well studied when all the networking nodes are always active. However, it is well-known that the nodes often switch between the active state and the sleep state to save energy. A node in duty-cycled scenarios with active/sleep cycles may require transmitting multiple times to send the message to all of its neighbors due to their different active times. MLAS in multihop wireless networks with Duty-Cycled scenarios (MLASDC) has also been well-studied under graph-based interference models such as the protocol interference model. To the best of our knowledge, no approximation algorithms have been proposed for MLASDC subject to physical interference. This is the first paper to develop efficient approximation algorithms for MLASDC subject to physical interference. The data aggregation schedule produced by our algorithm proposed in this paper achieves an approximation ratio at most a constant time of the length of a scheduling period if the maximum degree Δ of the network is bounded.

Many applications of wireless sensor networks (WSNs) are time-critical as well as requiring secure operations, and have serious consequences if the network is compromised. WSNs are often deployed in hostile environments where communication is monitored and the sensor nodes are subject to be compromised or manipulated by adversaries. For such WSNs, it is very important to have secure communications among the sensors. The m-composite key pre-distribution schemes proposed in [3] is one of the most popular mechanisms for communication security of WSNs. With such a security scheme, two nodes within each other's transmission range have a secure link between them if their key rings have at least m keys in common. In this paper, we develop an efficient scheduling algorithm for data gathering on secure WSNs. The link between two nearby sensors may not be secure and cannot be used for communication. Such a nature of secure WSNs makes the analysis of any scheduling algorithm for gathering much more challenging than on WSNs that can be modeled as disk graphs. To the best of our knowledge, this is the first paper that develops fast gathering schedules for multihop WSNs where the network topology cannot be modeled as a disk graph.

Billions of Internet of Things (IoT) devices, e.g., sensors and RFIDs, are arising around us providing not only computing-intensive, but also delay-sensitive services, ranging from augmented/virtual realities to distributed data analysis and artificial intelligence. Notably, the low response latency for IoT services is achieved at the cost of computing complexity that far exceeds the capabilities of IoT devices. To feed this trend, multiple computing paradigms are emerging, such as mobile transparent computing (TC), edge computing, and fog computing. These paradigms employ more resourceful edge devices, e.g., small-scale servers, smart phones, and laptops, to assist the low-end IoT devices. By offloading the computing-intensive tasks to the edge devices, it is expected to converge the data collection at IoT devices and the data processing at edge devices to provision computing-intensive and delay-sensitive services. However, many issues remain in the application of computing offloading which impede its flourishing in IoTs. To name a few, what are the killer APPs that need computing offloading for performance boost? How to partition an encapsulated APP into offloadable code blocks for remote loading? How to determine which code blocks or computing tasks should be offloaded to edge servers? How to customize the communication protocol to guarantee the coherence of computation offloading?

The explosive growth of content requests from mobile users is stretching the capability of current mobile networking technologies to satisfy users' demands with acceptable quality of service. An effective approach to address this challenge, which has not yet been thoroughly studied, is to offload network traffic by caching popular content at the edges (e.g., mobile devices and base stations) of mobile networks, thus reducing the massive duplication of content downloads. In this paper, we address the system modeling, large-scale optimization, and framework design of hierarchical edge caching in device-to-device aided mobile networks. In particular, taking into account the analysis of social behavior and preference of mobile users, heterogeneous cache sizes, and the derived system topology, we investigate the maximum capacity of the network infrastructure in terms of offloading network traffic, reducing system costs, and supporting content requests from mobile users locally. Our proposed framework has a low complexity and can be applied in practical engineering implementation. Trace-based simulation results demonstrate the effectiveness of the proposed framework.

Fractional Link scheduling is one of the most fundamental problems in wireless networks. The prevailing approach for shortest fractional link scheduling is based on a reduction to the maximum-weighted independent set problem, which itself may not admit efficient approximation algorithms. In addition, except for the wireless networks under the protocol interference model, none of the existing scheduling algorithms can produce a link schedule with explicit upper bounds on its length in terms of the link demands. As the result, the polynomial approximate capacity regions in these networks remain blank. This paper develops a purely combinatorial paradigm for fractional link scheduling in wireless networks. In addition to the superior efficiency, it is able to provide explicit upper bounds on the lengths of the produced link schedule. By exploiting these upper bounds, polynomial approximate capacity regions are derived. The effectiveness of this new paradigm is demonstrated by its applications in wireless networks under the physical interference model and wireless MIMO networks under the protocol interference model.

Consider a set of point-to-point communication requests in a multi-channel multihop wireless network, each of which is associated with a traffic demand of at most one unit of transmission time, and a weight representing the utility if its demand is fully met. A subset of requests is said to be schedulable without spectral splitting if they can be scheduled within one unit of time subject to the constraint each request is assigned with a unique channel throughout its transmission. This paper develops efficient and provably good approximation algorithms for finding a maximum-weighted subset of communication requests schedulable without spectral splitting.

Consider a set of point-to-point communication requests in a multi-channel multihop wireless network, each of which is associated with a traffic demand of at most one unit of transmission time, and a weight representing the utility if its demand is fully met. A subset of them is said to be feasible if they can be scheduled within one unit of time. The problem Maximum-Weighted Feasible Set (MWFS) seeks a feasible subset with maximum total weight together with a transmission schedule of them whose length is at most one unit of time. This paper develops efficient and provably good approximation algorithms for the problem MWFS.

For a time-sensitive application, the usefulness of its end results (also called the application's accrued utility value in the paper) depends on the time when the application is completed and its results are delivered. In this paper, we address the accrued utility value maximization problem for narrow parallel and time-sensitive applications. We first consider the problem in the context of a discrete time domain and present the Spatial-Temporal Interference Based (STIB) scheduling algorithm. We formally prove that the STIB algorithm is a 2-approximation algorithm. Second, we extend our work to a continuous time domain and present a heuristic scheduling algorithm, i.e., the Continuous Spatial-Temporal Interference Based (STIB-C) algorithm to maximize the system's total accrued utility value when the system operates in a continuous time domain. The extensive empirical evaluations reveal that: (1) in a discrete time domain, the systems' total accrued utility values obtained through the STIB algorithm are consistent with the theoretic bound, i.e., they never go below 50 percent of the optimal value. In fact, on average, the STIB algorithm can achieve over 92.5 percent of the optimal value; (2) compared to other scheduling policies listed in the literature, the developed STIB and STIB-C algorithms have clear advantages in terms of the system's total accrued utility value and the profitable application ratio. In particular, in terms of the system's total accrued utility value, both the STIB and the STIB-C algorithms achieve as much as six times for both the First Come First Come Serve(FCFS) with backfilling algorithm and the Gang Earliest Deadline First (EDF) algorithm, and 4.5 times for the 0-1 Knapsack based scheduling algorithm. In terms of the profitable application ratio, both the STIB and the STIB-C algorithms obtain as much as four times for both the FCFS with backfilling algorithm and the Gang EDF algorithm, and two times for the 0-1 Knapsack based scheduling algorithm.

Minimum-latency beaconing scheduling (MLBS) has been well studied when all the nodes are always awake. However, it is well-known that the networking nodes often switch between the active state and the sleep state to save energy. None of the known algorithms for MLBS are suitable for duty-cycled multihop wireless networks. In this paper, we study MLBS in duty-cycled multihop wireless networks (MLBSDC). Under the protocol interference model, we first present two constant-approx. algorithms for MLBSDC with the approx. bounds independent of |T|, the length of a scheduling period. Then, we develop an efficient algorithm for MLBSDC under the physical interference model. To the best of our knowledge, this is the first paper that develops constant-approx. algorithms for any communication scheduling with the approx. bounds independent of |T| when the duty-cycled scenarios are taken into consideration.

Motivated by many applications such as cognitive radio spectrum scheduling, downlink fading channel scheduling, and unmanned aerial vehicle dynamic routing, we study two restless bandit problems. Given a bandit consisting of multiple restless arms, the state of each arm evolves as a Markov chain. Assume each arm is associated with a positive weight. At each step, we select a subset of arms to play such that the weighted sum of the selected arms cannot exceed a limit. The reward of playing each arm varies according to the arm's state. The exact state of each arm is only revealed when the arm is played. The problem weighted restless bandit aims to maximize the expected average reward over the infinite horizon. We also study an extended problem called multiply-constrained restless bandit where each time there are two simultaneous constraints on the selected arms. First, the weighted sum of the selected arms cannot exceed a limit, Second, the number of the selected arms is at most a constant K. The objective of multiply-constrained restless bandit is to maximize the long term average reward. Both problems are partially observable Markov decision processes and have been proved to be PSPACE-hard even in their special cases. We propose constant approximation algorithms for both problems. Our method involves solving a semi-infinite program, converting back to a low-complexity policy, and accounting for the average reward via a Lyapunov function analysis.

Linear interference alignment (LIA) is one of the key interference mitigation techniques to enhance the wireless MIMO network capacity. The generic LIA feasibility amounts to whether or not a well-structured random matrix with entries drawn from a continuous distribution has full row-rank almost surely. Recently, a randomized algebraic test of feasibility was proposed in the literature. It is a pseudo-polynomial bounded-error probabilistic algorithm in nature, and has intrinsic limitations of requiring an inordinate amount of running time and memory even for a moderate sized input and being prone to round-off errors in floating-point computations. This paper presents necessary conditions and sufficient conditions of the generic LIA feasibility and develops fast and robust tests of them based on network flow. In certain settings, these conditions are both necessary and sufficient, and their flow-based tests yield efficient algorithm for feasibility test.

Multi-packet reception (MPR) technology provides a means of boosting wireless network capacity without requiring additional spectrum. It has received widespread attention over the past two decades from both industry and academic researchers. Despite the huge promise and considerable attention, provable good algorithms for maximizing network capacity in MPR-capable wireless networks are missing in the state of the art. One major technical obstacle is due to the complicated non-binary nature of the link independence; something which appears intractable with existing graph-theoretic methods. In this paper, we present practical polynomial-time approximation algorithms for variants of capacity optimization problems in MPR-capable wireless networks which achieve constant approximation bounds for the first time ever. In addition, polynomial-time approximation schemes are developed for those variants in wireless networks with constant-bounded MPR capabilities.

Multiflow problems are one of the most fundamental problems in both wired networks and wireless networks. Due to the cross-layer nature, multiflow problems in wireless networks are significantly harder than their counterparts in wired networks and have received much research interest over the past decade. Common to most other early-staged research, the characterization of computational hardness and the “war” on achievable approximation bounds have been the priority to the existing studies of multiflow problems in wireless networks while their practical feasibility in both running time and memory requirement is ignored as long they are polynomial. In fact, almost all of the state-of-the-art approximation algorithms for multiflow problems in wireless networks are all resorted to the traditional linear programming (LP) methods exclusively. However, those traditional LP methods can require an inordinate amount of running time and memory even for a moderate sized input, and consequently they often prove unusable in practice. This paper presents a completely new paradigm for multiflow problems in general wireless networks which is radically different from the prevailing LP-based paradigm, and develops practical algorithmic solutions which are much faster and simpler.

Beaconing is a primitive communication task in which every node locally broadcasts a packet to all of its neighbors within a fixed distance. The problem Minimum Latency Beaconing Schedule (MLBS) seeks a shortest schedule for beaconing subject to the interference constraint. MLBS has been well studied when all the nodes are always awake. However, it is well-known that the networking nodes often switch between the active state and the sleep state to save energy. A node in duty-cycled scenarios may require transmitting multiple times to inform all of its neighbors due to their different active times. Thus, all of the known algorithms for MLBS are not suitable for duty-cycled multihop wireless networks. In this paper, we study MLBS in Duty-Cycled multihop wireless networks (MLBSDC). We first present two constant-approximation algorithms for MLBSDC under the protocol interference model with the approximation bounds independent of the length of a scheduling period. Then, we develop an efficient algorithm for MLBSDC under the physical interference model. To the best of our knowledge, this is the first paper that develops efficient algorithms for MLBSDC under either of these two interference models.

Finding a maximum-weighted independent set of links is a fundamental problem in wireless networking and has broad applications in various wireless link scheduling problems. Under protocol interference model, it is NP-hard even when all nodes have uniform (and fixed) interference radii and the positions of all nodes are available. On one hand, it admits a polynomial-time approximation scheme (PTAS). In other words, for any fixed ε > 0, it has a polynomial-time (depending on ε) (1 + ε)-approximation algorithm. However, such PTAS is of theoretical interest only and is quite infeasible practically. On the other hand, only with the uniform interference radii is a simple (greedy) constant-approximation algorithm known. For the arbitrary interference radii, fast constant-approximation algorithms are still missing. In this paper, we present a number of fast and simple approximation algorithms under the general protocol interference model. When applied to the plane geometric variants of the protocol interference model, these algorithms produce constant-approximate solutions efficiently.

Maximum multiflow and maximum concurrent mul-tiflow in multi-channel multi-radio (MC-MR) wireless networks have been well-studied in the literature. They are NP-hard even in single-channel single-radio (SC-SR) wireless networks when all nodes have uniform (and fixed) interference radii and the positions of all nodes are available. While they admit a polynomial-time approximation scheme (PTAS) when the number of channels is bounded by a constant, such PTAS is quite infeasible practically. Other than the PTAS, all other known approximation algorithms, in both SC-SR wireless networks and MC-MR wireless networks, resorted to solve a polynomial-sized linear program (LP) exactly. The scalability of their running time is fundamentally limited by the general-purposed LP solvers. In this paper, we first introduce the concept of interference costs and prices of a path and explore their relations with the maximum (concurrent) multiflow. Then we develop purely combinatorial approximation algorithms which compute a sequence of least interference-cost routing paths along which the flows are routed. These algorithms are faster and simpler, and achieve nearly the same approximation bounds known in the literature.

For a time-sensitive application, the usefulness or the quality of the application's end result depends on the time when the result is delivered, or when the application is completed. A Time Utility Function (TUF) is often used to represent the dependency between an application's accrued value and its completion time. For parallel and time-sensitive applications, each application has multiple tasks that must be executed concurrently in order to produce a result. Therefore, their execution occupies resources in two dimensions: spatial, i.e., the number of processing units needed to support concurrent tasks, and temporal, i.e., time duration needed to complete the application. Because of the parallelism and time-sensitive features of the applications, the execution interference among parallel and time-sensitive applications can be both in spatial and temporal domains. In this paper, we first introduce a metric to measure the spatial-temporal interference on applications' accrued values. Second, based on the metric, we develop a scheduling algorithm, i.e., the Discounting Spatial-Temporal Interference (DSTI) scheduling algorithm, to maximize system's total accrued utility value for a given set of parallel and time-sensitive applications. Our simulation results show that the proposed DSTI algorithm results in close to optimal solutions and also has clear advantage over existing approaches in the literature in terms of system total accrued utility values and profitable application ratio. It accrues up to 164%, 150%, and 97% more system value, and up to 21%, 35%, and 18% higher profitable application ratio than the Gang EDF, the FCFS with backfilling, and the 0-1 Knapsack based scheduling algorithms, respectively.

Multiple-input multiple-output (MIMO) technology provides a means of boosting network capacity without requiring additional spectrum. It has received widespread attention over the past decade from both industry and academic researchers, now forming a key component of nearly all emerging wireless standards. Despite the huge promise and considerable attention, a rigorous algorithm-theoretic framework for maximizing network capacity in multihop wireless MIMO\ networks is missing in the state of the art. The existing algorithms and protocols for maximizing network capacity in multihop wireless MIMO networks are purely heuristic without any provable performance guarantees. In this paper we conduct a comprehensive algorithm study for maximizing network capacity in multihop wireless MIMO networks with receiver-side interference suppression, including the full characterization of NP-hardness and APX-hardness, the polynomial time approximation schemes, and the practical approximation algorithms with provable performance guarantees.

One of the most fundamental tasks of wireless sensor networks is to provide coverage of the deployment region. We study the coverage of a line interval with a set of wireless sensors with adjustable coverage ranges. Each coverage range of a sensor is an interval centered at that sensor whose length is decided by the power the sensor chooses. The objective is to find a range assignment with the minimum cost. There are two variants of the optimization problem. In the discrete variant, each sensor can only choose from a finite set of powers, whereas in the continuous variant, each sensor can choose power from a given interval. For the discrete variant of the problem, a polynomial-time exact algorithm is designed. For the continuous variant of the problem, NP-hardness of the problem is proved and followed by an ILP formulation. Then, constant-approximation algorithms are designed when the cost for all sensors is proportional to r κ for some constant κ ≥ 1, where r is the covering radius corresponding to the chosen power. Specifically, if κ = 1, we give a 1.25-approximation algorithm and a fully polynomial-time approximation scheme; if κ > 1, we give a 2-approximation algorithm. We also show that the approximation analyses are tight.

For wireless link scheduling in multi-channel multi-radio wireless networks aiming at maximizing (concurrent) multi-flow, constant-approximation algorithms have recently been developed in [11]. However, the running time of those algorithms grows quickly with the number of radios per node (at least in the sixth order) and the number of channels (at least in the cubic order). Such poor scalability stems intrinsically from the exploding size of the fine-grained network representation upon which those algorithms are built. In this paper, we introduce a new structure, termed as concise conflict graph, on the node-level links directly. Such structure succinctly captures the essential advantage of multiple radios and multiple channels. By exploring and exploiting the rich structural properties of the concise conflict graphs, we are able to develop fast and scalable link scheduling algorithms for either minimizing the communication latency or maximizing the (concurrent) multi-flow. These algorithms have running time growing linearly in both the number of radios per node and the number of channels, while not sacrificing the approximation bounds.

Maximizing the wireless network capacity under physical interference model is notoriously hard due to the nonlocality and the additive nature of the wireless interference under the physical interference model. This problem has been extensively studied recently with the achievable approximation bounds progressively improved from the linear factor to logarithmic factor. It has been a major open problem whether there exists a constant-approximation approximation algorithm for maximizing the wireless network capacity under the physical interference model. In this paper, we improve the status quo for the case of linear transmission power assignment, which is widely adopted due to its advantage of energy conservation. By exploring and exploiting the rich nature of the wireless interference with the linear power assignment, we develop constant-approximation algorithms for maximizing the wireless network capacity with linear transmission power assignment under the physical interference model, in both the unidirectional mode and the bidirectional mode.

Static greedy link schedulings have much simpler implementation than dynamic greedy link schedulings such as Longest-queue-first (LQF) link scheduling. However, its stability performance in multi-channel multi-radio (MC-MR) wireless networks is largely under-explored. In this paper, we present a stability subregion with closed form of a static greedy link scheduling in MC-MR wireless networks under the 802.11 interference model. By adopting some special static link orderings, the stability subregion is within a constant factor of the stable capacity region of the network. We also obtain constant lower bounds on the throughput efficiency ratios of the static greedy link schedulings in some special static link orderings.

Connected dominating set (CDS) has a wide range of applications in multihop wireless networks. The Minimum CDS problem has been studied extensively in multihop wireless networks with uniform communication ranges. However, in practice, the nodes may have different communication ranges either because of the heterogeneity of the nodes, or due to interference mitigation, or due to a chosen range assignment for energy conservation. In this paper, we present a greedy approximation algorithm for computing a Minimum CDS in multihop wireless networks with disparate communications ranges and prove that its approximation ratio is better than the best one known in the literature. Our analysis utilizes a tighter relation between the independence number and the connected domination number.

We are in an age where people are paying increasing attention to energy conservation around the world. The heating and air-conditioning systems of buildings introduce one of the largest chunks of energy expenses. In this article, we make a key observation that after a meeting or a class ends in a room, the indoor temperature will not immediately increase to the outdoor temperature. We call this phenomenon thermal inertia . Thus, if we arrange subsequent meetings in the same room rather than in a room that has not been used for some time, we can take advantage of such undissipated cool or heated air and conserve energy. Though many existing energy conservation solutions for buildings can intelligently turn off facilities when people are absent, we believe that understanding thermal inertia can lead system designs to go beyond on-and-off-based solutions to a wider realm. We propose a framework for exploring thermal inertia in room management. Our framework contains two components. (1) The energy-temperature correlation model captures the relation between indoor temperature change and energy consumption. (2) The energy-aware scheduling algorithms: given information for the relation between energy and temperature change, energy-aware scheduling algorithms arrange meetings not only based on common restrictions, such as meeting time and room capacity requirement, but also energy consumptions. We identify the interface between these components so further works towards same on direction can make efforts on individual components. We develop a system to verify our framework. First, it has a wireless sensor network to collect indoor, outdoor temperature and electricity expenses of the heating or air-conditioning devices. Second, we build an energy-temperature correlation model for the energy expenses and the corresponding room temperature. Third, we develop room scheduling algorithms. In detail, we first extend the current sensor hardware so that it can record the electricity expenses in re-heating or re-cooling a room. As the sensor network needs to work unattendedly, we develop a hardware board for long-range communications so that the Imote2 can send data to a remote server without a computer relay close by. An efficient two-tiered sensor network is developed with our extended Imote2 and TelosB sensors. We apply laws of thermodynamics and build a correlation model of the energy needed to re-cool a room to a target temperature. Such model requires parameter calibration and uses the data collected from the sensor network for model refinement. Armed with the energy-temperature correlation model, we develop an optimal algorithm for a specified case, and we further develop two fast heuristics for different practical scenarios. Our demo system is validated with real deployment of a sensor network for data collection and thermodynamics model calibration. We conduct a comprehensive evaluation with synthetic room and meeting configurations, as well as real class schedules and classroom topologies of The Hong Kong Polytechnic University, academic calendar year of Spring 2011. We observe 20% energy savings as compared with the current schedules.

We are in an age where people are paying increasing attention to energy conservation around the world. The heating and air-conditioning systems of buildings introduce one of the largest chunk of energy expenses. In this paper, we make a key observation that after a meeting or a class ends in a room, the indoor temperature will not immediately increase to the outdoor temperature. We call this phenomenon Thermal Inertia. Thus, if we arrange subsequent meetings in the same room; than a room that has not been used for some time, we can take advantage of such un-dissipated cool or heated air and conserve energy. We develop a green room management system with three main components. First, it has a wireless sensor network to collect indoor, outdoor temperature and electricity expenses of the air-conditioning devices. Second, we build an energy-temperature correlation model for the energy expenses and the corresponding room temperature. Third, we develop room scheduling algorithms. Our system is validated with real deployment of a sensor network for data collection and thermodynamics model calibration. We conduct a comprehensive evaluation with synthetic room and meeting configurations. We observe a 30% energy saving as compared with the current schedules.

This paper addresses the joint selection and power assignment of a largest set of given links which can communicate successfully at the same time under the physical interference model in the duplex (i.e. bidirectional) mode. For the special setting in which all nodes have unlimited maximum transmission power, Halldorsson and Mitra [5] developed an approximation algorithm with a huge constant approximation bound. For the general setting in which all nodes have bounded maximum transmission power, the existence of constant approximation algorithm remains open. In this paper, we resolve this open problem by developing an approximation algorithm which not only works for the general setting of bounded maximum transmission power, but also has a much smaller constant approximation bound.

Data aggregation, as a primitive communication task in wireless networks, can reduce the communication complexity. However, in-network aggregation usually brings an unavoidable security defect. Some malicious nodes may control a large percentage of the whole network data and compel the network misbehave in an arbitrary manner. Thus, locating the malicious nodes to prevent them from further disaster is a practical challenge for data aggregation schemes. Based on the grouping and localization techniques, we propose a novel integrated protocol to locate malicious nodes. The proposed protocol does not rely on any special hardware and requests only incomplete information of the network from the security schemes. We also conduct simulation study to evaluate the proposed protocol.

Longest-queue-first (LQF) link scheduling is a greedy link scheduling in multihop wireless networks. Its stability performance in single-channel single-radio (SC-SR) wireless networks has been well studied recently. However, its stability performance in multi-channel multi-radio (MC-MR)wireless networks is largely under-explored. In this paper, we present a stability subregion with closed form of the LQF scheduling in MC-MR wireless networks, which is within a constant factor of the network stability region. We also obtain constant lower bounds on the efficiency ratio of the LQF scheduling in MC-MR wireless networks under the 802.11 interference model or the protocol interference model.

Broadcasting is a fundamental operation in wireless networks and plays an important role in the communication protocol design. In multihop wireless networks, however, interference at a node due to simultaneous transmissions from its neighbors makes it nontrivial to design a minimum-latency broadcast algorithm, which is known to be NP-complete. We present a simple 12-approximation algorithm for the one-to-all broadcast problem that improves all previously known guarantees for this problem. We then consider the all-to-all broadcast problem where each node sends its own message to all other nodes. For the all-to-all broadcast problem, we present two algorithms with approximation ratios of 20 and 34, improving the best result available in the literature. Finally, we report experimental evaluation of our algorithms. Our studies indicate that our algorithms perform much better in practice than the worst-case guarantees provided in the theoretical analysis and achieve up to 37 percent performance improvement over existing schemes.

In this paper, we study periodic query scheduling for data aggregation with minimum delay under various wireless interference models. Given a setQof periodic aggregation queries, each queryQi∈Qhas its own periodpiand the subset of source nodesSicontaining the data. We first propose a family of efficient and effective real-time scheduling protocols that can answer every job of each query taskQi∈Qwithin a relative delayO(pi) under resource constraints by addressing the following tightly coupled tasks: routing, transmission plan constructions, node activity scheduling, and packet scheduling. Based on our protocol design, we further propose schedulability test schemes to efficiently and effectively test whether, for a set of queries, each query job can be finished within a finite delay. Our theoretical analysis shows that our methods achieve at least a constant fraction of the maximum possible total utilization for query tasks, where the constant depends on wireless interference models. We also conduct extensive simulations to validate the proposed protocol and evaluate its practical performance. The simulations corroborate our theoretical analysis.

It is very challenging to compute the capacity region of a multi-radio multi-channel (MR-MC) network, which involves complex resource contention including the co-channel interferences and radio interface contentions. In this paper, we study the local sufficient rate constraints that can be constructed at each network node in a distributed manner to ensure a feasible flow allocation for the MR-MC network. The analysis of capacity region with the rate constraints is facilitated by our tool of multi-dimensional conflict graph (MDCG), which systematically describes all kinds of conflict relationships in an MR-MC network. Specially, we establish two types of local sufficient constraints, the neighborhood constraint and the sufficient clique constraint, respectively; and both types can ensure a constant portion of the optimal capacity region, termed as capacity efficiency ratio. The capacity efficiency ratios associated with the neighborhood constraint and the sufficient clique constraint are related to the analysis of the interference degree and the imperfection ratio of an MDCG, respectively. A specific challenge is that methodology computing the interference degree and the imperfection ratio of single-radio single-channel (SR-SC) networks could not be directly extended to the MR-MC context, because MR-MC network has disruptively different geometric properties compared to the SR-SC network: In an MR-MC network, the geometric closeness does not necessarily imply interference due to possible parallel transmissions over different radios and channels. The fundamental contributions of this paper are the theoretical studies of the interference degree and the imperfection ratio of an MDCG, revealing how such graphical characteristics are related to those in the SR-SC context under the impact of the MR-MC geometric property. We also present extensive numerical results to demonstrate the effectiveness of the proposed local sufficient constraints in ensuring a larger capacity region compared to the well-known results in.

This paper studies maximum multiflow (MMF) and maximum concurrent multiflow (MCMF) in muliti-channel multi-radio multihop wireless networks under the 802.11 interference model or the protocol interference model. We introduce a fine-grained network representation of multi-channel multi-radio multihop wireless networks and present some essential topological properties of its associated conflict graph. By exploiting these properties, we develop practical polynomial approximation algorithms for MMF and MCMF with constant approximation bounds regardless of the number of channels and radios. Under the 802.11 interference model, their approximation bounds are at most 20 in general and at most 8 with uniform interference radii; under the protocol interference model, if the interference radius of each node is at least c times its communication radius, their approximation bounds are at most 2 (⌈π/ arcsin c-1/2c⌉ + 1). In addition, we also prove that if the number of channels is bounded by a constant (which is typical in practical networks), both MMF and MCMF admit a polynomial-time approximation scheme under the 802.11 interference model or under the protocol interference model with some additional mild conditions.

Link scheduling is a fundamental problem in multihop wireless networks because the capacities of the communication links in multihop wireless networks, rather than being fixed, vary with the underlying link schedule subject to the wireless interference constraint. The majority of algorithmic works on link scheduling in multihop wireless networks assume binary interference models such as the 802.11 interference model and the protocol interference model, which often put severe restrictions on interference constraints for practical applicability of the link schedules. On the other hand, while the physical interference model is much more realistic, the link scheduling problem under physical interference model is notoriously hard to resolve and been studied only recently by a few works. This paper conducts a full-scale algorithmic study of link scheduling for maximizing throughput capacity or minimizing the communication latency in multihop wireless networks under the physical interference model. We build a unified algorithmic framework and develop approximation algorithms for link scheduling with or without power control.

Longest Queue First (LQF) is a well-known link scheduling strategy in multihop wireless networks. Its throughput efficiency ratio was shown to be exactly the local pooling factor (LPF) of the multihop wireless network in a recent seminar work by Joo et al.. Under the 802.11 interference model with uniform interference radii, the LPF of a multihop wireless network was known to be at least 1/6. However, little is known about the LPF of a multihop wireless network under the 802.11 interference model with arbitrary interference radii or under the protocol interference model. In this paper, we derive constant lower bounds on LPFs of these multihop wireless networks. Specifically, under the 802.11 interference model with arbitrary interference radii, the LPF is at least 1/16. Under the protocol interference model, if the communication radius of each node is at most c times its interference radius for some c <; 1, then the LPF is at least 1/ (2 ⌈π/ arcsin 1-c/2⌈ - 1)).

Link scheduling is a fundamental design issue in multihop wireless networks. All existing link scheduling algorithms require the precise information of the positions, and/or communication/interference radii of all nodes. For practical networks, it is not only difficult or expensive to obtain these parameters, but also often impossible to get their precise values. The link scheduling determined by the imprecise values of these parameters may fail to guarantee the same approximation bounds of the link scheduling determined by precise values. Therefore, the existing link scheduling algorithms lack performance robustness. In this paper, we propose a robust link scheduling, which can be easily computed with only the information on whether a given pair of links have conflict or not and therefore is robust. In addition, our link scheduling does not compromise the approximation bound and indeed sometimes can achieve better approximation bound. Particularly, under the 802.11 interference model, its approximation bound is 16 in general and 6 with uniform interference radii, an improvement over the respective best-known approximation bounds 23 and 7.

Consider a random multihop wireless network represented by a Poisson point process over a unit-area disk with mean n. Let øndenote its critical transmission radius for its greedy forward routing. Recently, asymptotic bounds on ønhave been progressively improved. However, the precise asymptotic probability distribution of ønremains open. In this paper, we settle this open problem. Specifically, let σ = 2π/3 - √3/2. Then for any constant c, the asymptotic probability of equation is proved to be exactly exp (-(1/σ/π-1/3-π/2σ)e-c).

One of the most fundamental task of wireless networks is to provide coverage of a set of targets. Suppose that all nodes and targets lie in a plane, and all nodes have circular coverage ranges of arbitrary radii. The problem Minimum Wireless Cover (MWC) seeks the fewest nodes to cover the targets. If all nodes are associated with some positive prices, the problem Cheapest Wireless Cover (CWC) seeks a cheapest set of nodes to cover the targets. If all nodes have bounded lives, the problem Max-Life Wireless Cover (MLWC) seeks wireless coverage schedule of maximum life subject to the life constraints of individual nodes. In this paper, we present a polynomial time approximation scheme (PTAS) for MWC, and two randomized 2O(log* n)-approximation algorithms for CWC and MLWC respectively, where n is the number of nodes, and log* n is the iterated logarithm of n with base 2.

We address a new and general maximal lifetime problem in sensor-target surveillance. We assume that each sensor can watch at most k targets (k ≥ 1) and each target should be watched by h sensors (h ≥ 1) at any time. The problem is to schedule sensors to watch targets and forward the sensed data to a base station such that the lifetime of the surveillance network is maximized. This general problem includes the existing ones as its special cases (k = 1 and h = 1 in and k = 1 and h ≥ 2 in). It is also important in practice because some sensors can monitor multiple or all targets within their surveillance ranges and multisensor fusion (i.e., watching a target by multiple sensors) gives better surveillance results. The problem involves several subproblems and one of them is a new matching problem called (k, h)-matching. The (k, h)-matching problem is a generalized version of the classic bipartite matching problem (when k = h = 1, (k, h)-matching becomes bipartite matching). We design an efficient (k, h)-matching algorithm to solve the (k, h)-matching problem and then solve the general maximal lifetime problem. As a byproduct of this study, the (k, h)-matching problem and the proposed (k, h)-matching algorithm can potentially be applied to other problems in computer science and operations research.

Optimal capacity analysis in multi-radio multi-channel wireless networks by nature incurs the formulation of a mixed integer programming, which is NP-hard in general. The current state of the art mainly resorts to heuristic algorithms to obtain an approximate solution. In this paper, we propose a novel concept of multi-dimensional conflict graph (MDCG). Based on MDCG, the capacity optimization issue can be accurately modeled as a linear programming (LP) multi-commodity flow (MCF) problem, augmented with maximal independent set (MIS) constraints. The MDCG-based solution will provide not only the maximum throughput or utility, but also the optimal configurations on routing, channel assignment, and scheduling. Moreover, the MDCG-based optimal capacity planning can exploit dynamic channel swapping, which is difficult to achieve for those existing heuristic algorithms. A particular challenge associated with the MDCG-based capacity analysis is to search exponentially many possible MISs. We theoretically show that in fact only a small set of critical MISs, termed as critical MIS set, will be scheduled in the optimal resource allocation. We then develop a polynomial computing method, based on a novel scheduling index ordering (SIO) concept, to search the critical MIS set. Extensive numerical results are presented to demonstrate the efficiency of the MDCG-based resource allocation compared to well-known heuristic algorithm presented in, and the efficiency of SIO-based MIS computing compared to the widely adopted random algorithm for searching MISs.

Transmission power plays a crucial role in the design and performance of wireless networks. The issue is therefore complex since an increase in transmission power implies that a high quality signal is received at the receiver and hence an increase in channel capacity. Conversely, due to the shared nature of the wireless medium an increase in transmission power also implies high interference in the surrounding region and hence a quadratic reduction in the capacity of wireless networks. Recent literatures indicate that employing multiple channels can mitigate the negative effects of wireless interference and thus greatly improve the overall network capacity. Therefore, it is worth investigating the effect of exploiting power on the capacity of multi-channel multi-radio (MC-MR) wireless networks. Specifically, in this paper we address the following questions: (a) Can we maximize the capacity of MC-MR wireless networks by exploiting power? (b) Under what criteria can we increase the transmission power of the nodes in a MC-MR network? When n nodes each with m half-duplex interfaces are optimally deployed in a torus of unit area, traffic patterns are optimally assigned, each transmission's range is optimally chosen and in the presence of c channels, we show that in contrast to the setting where nodes transmit at minimum power level Po the transport capacity, measured in bit-meters per second, of MC-MR network exploiting power is increased by Θ(cmin) in region cmin0(c/cmin)α/2and P0nα/2respectively-where cminis the minimum number of channels required to achieve conflict-free transmissions in a network. Our analysis also sheds light into several insights that designers may want to consider to improve the performance of energy-efficient bandwidth-constrained wireless networks.

This paper studies the maximum throughput that can be supported by a given wireless mesh backhaul network, over a practical CSMA/CA medium access control (MAC) protocol. We resort to the multi-commodity flow (MCF) formulation, augmented with the conflict-graph constraints, to jointly compute the maximum throughput and the associated optimal network dimensioning; while use a novel approach to take into account the collision overhead in the distributed CSMA/CA MAC. Such overhead has been ignored by the existing MCF-based capacity studies, which assume impractical centralized scheduling and result in aggressive network dimensioning, unachievable over the CSMA/CA MAC. We develop a generic method to integrate the CSMA/CA MAC analysis with the MCF formulation for optimal network capacity analysis, and derive both an upper bound and a lower bound of the network throughput over a practical CSMA/CA protocol. To the best of our knowledge, this paper is the first rigorous theoretical study of the achievable capacity over a multi-hop CSMA/CA based wireless network.

Beaconing is a primitive communication task in which every node locally broadcasts a packet to all its neighbors within a fixed distance. Assume that all communications proceed in synchronous time-slots and each node can transmit at most one fixed-size packet in each time-slot. The problem Minimum-latency beaconing schedule (MLBS) in multihop wireless networks seeks a shortest schedule for beaconing subject to the interference constraint. MLBS has been intensively studied since the mid-1980s, but all assume the protocol interference model with uniform interference radii. In this paper, we first present a constant-approximation algorithm for MLBS under the protocol interference model with arbitrary interference radii. Then, we develop a constant-approximation algorithm for MLBS under the physical interference model. Both approximation algorithms have efficient implementations in a greedy first-fit manner.

The capacity region of multihop wireless network is involved in many capacity optimization problems. However, the membership of the capacity region is NP-complete in general, and hence the direct application of capacity region is quite limited. As a compromise, we often substitute the capacity region with a polynomial approximate capacity subregion. In this paper, we construct polynomial ¿-approximate capacity subregions of multihop wireless network under either 802.11 interference model or protocol interference model in which all nodes have uniform communication radii normalized to one and uniform interference radii ¿ ¿ 1. The approximation factor ¿ decreases with ¿ in general and is smaller than the best-known ones in the literature. For example, ¿ = 3 when ¿ ¿ 2.2907 under the 802.11 interference model or when ¿ ¿ 4.2462 under the protocol interference model. Our construction exploits a nature of the wireless interference called strip-wise transitivity of independence discovered in this paper and utilize the independence polytopes of cocomparability graphs in a spatial-divide-conquer manner. We also apply these polynomial ¿-approximate capacity subregions to compute ¿-approximate solutions for maximum (concurrent) multiflows.

Shortest link scheduling (SLS) in multihop wireless networks under physical interference model is notoriously hard to resolve and been studied only recently by a few works. Most of the obtained approximation bounds grow linearly with the number of links, and many are only valid with single-hop wireless networks, and some claimed approximation bounds are even false. This paper conducts a rigorous algorithmic study of SLS with power control under the physical interference model. We develop a polynomial O (βlnα)-approximation algorithm for SLS, where α is the independence number and β is the power diversity.

In grid routing, the plane is tessellated into equal-sized square cells.Two cells are called neighbor cells if they share a common edge, and two nodes are called routing neighbors if they are in neighbor cells and within each other's transmission range.If communication parties are in the same cell, packets can be transmitted directly; otherwise, packets are forwarded to routing neighbors that are in cells closer to destination cells.As a greedy strategy, grid routing suffers the existence of local minima at which no neighbor nodes exist for relaying packets.To guarantee deliverability, in this paper, we investigate two vital parameters of grid routing, called the grid size and the transmission radius.Assume that nodes are represented by a Poisson point process with rate n over a unit-area square, and let l denote the grid size and r the transmission radius.First, we show that if l = β ln n/n for some constant β and r = √ 5l, then β = 1 is the threshold for deliverability.In other words, there almost surely do not exist local minima if β > 1 and there almost surely exist local minima if β < 1. Next, for any given β > 1, we give sufficient and necessary conditions to determine the critical transmission radius (CTR) for deliverability.Then, we show that as β ∼ = 1.092, the CTR r ∼ = 2.09 √ ln n/n is the minimum over all β > 1. Simulation results are given to validate this theoretical work.

In multi-hop wireless networks, the use of virtual backbone can greatly simplify routing, broadcasting, as well as energy/bandwidth saving. However, constructing a virtual backbone is costly and time-consuming because of the inevitable transmission interference during the process of the construction. In the literature, most of virtual backbone construction algorithms did not take the interference issue into consideration. To the best of our knowledge, our proposed algorithm is the first fully-distributed, interference-aware virtual backbone construction algorithm that has a proven bound on the construction latency. Besides, our proposed algorithm can be applied to the leader election problem, and such application results in a fully-distributed and interference-aware leader election algorithm of time complexity O(n \log n) (where n is the number of nodes). This new leader election algorithm is practical in wireless networks because interference has already been dealt with; is also results in the fastest interference-aware leader election algorithm to the best of our knowledge.

A range assignment to the nodes in a wirelessad hocnetwork induces a topology in which there is an edge between two nodes if and only if both of them are within each other's transmission range. The critical transmission radius fork-connectivity is the smallestrsuch that if all nodes have the transmission radiusr, the induced topology isk-connected. In this paper, we study the asymptotic critical transmission radius fork-connectivity in a wirelessad hocnetwork whose nodes are uniformly and independently distributed in a unit-area square or disk. We provide a precise asymptotic distribution of the critical transmission radius fork-connectivity. In addition, the critical neighbor number fork-connectivity is the smallest integerlsuch that if every node sets its transmission radius equal to the distance between itself and itsl-th nearest neighbor, the induced (symmetric) topology isk-connected. Applying the critical transmission radius fork-connectivity, we can obtain an asymptotic almost sure upper bound on the critical neighbor number fork-connectivity.

We studied the minimum latency gossiping (all-to-all broadcast) problem in multihop radio networks defined as follows: Each node in the network is preloaded with a message and the objective is to distribute each node's message to the entire network with minimum latency. We studied this problem in the unit-size message model and the unit disk graph model. The unit-size model means different messages cannot be combined as one message, and the unit disk graph model means a link exists between two nodes if and only if their euclidean distance is less than 1. The minimum latency gossiping problem is known to be NP-hard in these two models. In this work, we designed a gossiping scheme that significantly improved all current gossiping algorithms in terms of the approximation ratio. Our work has approximation ratio 27, a great improvement of the current state-of-the-art algorithm (which has ratio 1,947). We also discussed the single point of failure problem and its impact on our approximation ratio. We designed an amended gossiping algorithm with ratio 27 in case of a nonsource node failure. We also designed an amended gossiping algorithm with ratio 29 in case of source failure.

In this paper, we study the minimum-latency broadcast scheduling problem in the probabilistic model. We establish an explicit relationship between the tolerated transmission-failure probability and the latency of the corresponding broadcast schedule. Such a tolerated transmission-failure probability is calculated in the strict sense that the failure to receive the message at any single node will lead to the entire broadcast failure and only if all nodes have successfully received the message do we consider it a success. We design a novel broadcast scheduling algorithm such that the broadcast latency is evaluated under such a strict definition of failure. The latency bound we derive is a strong result in the sense that our algorithm achieves a low broadcast latency under this rather strict broadcast-failure definition. Simulation results are also provided to justify our derived theoretical latency bound.

In wireless ad hoc networks, relative neighborhood graphs (RNGs) are widely used for topology control. If every node has the same transmission radius, then an RNG can be locally constructed by using only one hop information if the transmission radius is set no less than the largest edge length of the RNG. The largest RNG edge length is called the critical transmission radius for the RNG. In this paper, we consider the RNG over a Poisson point process with mean density ¿ in a unit-area disk. Let ß0= ¿(1/(2/3 - ¿(3)/2¿)) ¿ 1.6. We show that the largest RNG edge length is asymptotically almost surely at most ß ¿(1n n/¿n) for any fixed ß > ß0and at least ß ¿(1n n/¿n) for any fixed ß0. This implies that the threshold width of the critical transmission radius is o (¿(1n n/n)). In addition, we also prove that for any constant ¿, the expected number of RNG edges whose lengths are not less than ß0¿(1n n+¿)/¿n is asymptotically equal to ß02/2 e-¿.

The paper addresses the maximal lifetime problem in sensor-target surveillance networks. Given a set of sensors and targets in an Euclidean plane, each sensor can watch all targets within its surveillance range and each target should be watched by at least one sensor at any time. The problem is to schedule the sensors to watch the targets and forward the sensed data to the base station, such that the lifetime of the surveillance network is maximized, where the lifetime is the duration that all targets are watched and all active sensors are connected to the base station. We propose an optimal solution to achieve the maximal lifetime. Our solution consists of three steps: 1) compute the maximal lifetime of the surveillance network and find a workload matrix and data flows by using the linear programming technique; 2) decompose the workload matrix into a sequence of schedule matrices by using the perfect matching technique; 3) determine the sensor-target surveillance trees based on the above obtained schedule matrices and data flows, which specify the active sensors and the routes to pass sensed data to the base station. The proposed optimal solution is illustrated by a numeric example.

Broadcasting is a fundamental operation in wireless networks and plays an important role in the communication protocol design. In multihop wireless networks, however, interference at a node due to simultaneous transmissions from its neighbors makes it non-trivial to design a minimum-latency broadcast algorithm, which is known to be NP-complete. We present a simple 12-approximation algorithm for the one-to-all broadcast problem that improves all previously known guarantees for this problem. We then consider the all-to-all broadcast problem where each node sends its own message to all other nodes. For the all-to-all broadcast problem, we present two algorithms with approximation ratios of 20 and 34, improving the best result available in the literature. Finally, we report experimental evaluation of our algorithms. Our studies indicate that our algorithms perform much better in practice than the worst-case guarantees provided in the theoretical analysis and achieve up to 37% performance improvement over existing schemes.

Minimum-latency beaconing schedule (MLBS) in synchronous multihop wireless networks seeks a schedule for beaconing with the shortest latency. This problem is NP-hard even when the interference radius is equal to the transmission radius. All prior works assume that the interference radius is equal to the transmission radius, and the best-known approximation ratio for MLBS under this special interference model is 7. In this paper, we present a new approximation algorithm called strip coloring for MLBS under the general protocol interference model. Its approximation ratio is at most 5 when the interference radius is equal to transmission radius, and is between 3 and 6 in general.

In this paper, we present short communication schedules for broadcast, data aggregation, data gathering, and gossiping in multihop wireless networks subject to physical interference. We assume that all communications proceed in synchronous time-slots, each node can transmit at most one packet of fixed size in each time-slot, and all nodes have fixed and equal transmission power. Under mild assumptions, all of our communication schedules for those four group communications have constant approximation bounds. These communication schedules are built upon a general technique which enables a unified graph-theoretic treatment of the communication scheduling subject to the physical interference constraint.

This paper studies maximum multicommodity flow and maximum concurrent flow in multihop wireless networks subject to both bandwidth and interference constraints. The existing proof of the NP-hardness of both problems is too contrived to be applicable to meaningful multihop wireless networks. In addition, all known constant-approximation algorithms for both problems restricted to various network classes are super-exponential in running time. Some of them are simply incorrect. In this paper, we first provide a rigorous proof of the NP-hardness of both problems even in very simple settings. Then, we show that both problems restricted to a broad family of multihop wireless networks admit polynomial-time approximation scheme (PTAS). After that, we develop a unified framework for the design and analysis of polynomial approximation algorithms for both problems. Following such framework, we obtain polynomial constant-approximation algorithms for both problems restricted to a broad network family. The approximation ratios of these algorithms are also better than those known in the literature.

Minimum-latency aggregation schedule (MLAS) in synchronous multihop wireless networks seeks a shortest schedule for data aggregation subject to the interference constraint. In this paper, we study MLAS under the protocol interference model in which each node has a unit communication radius and an interference radius ρ ≥ 1. All known aggregation schedules assumed ρ = 1, and the best-known aggregation latency with ρ = 1 is 23R + Δ - 18 where R and Δ are the radius and maximum degree of the communication topology respectfully. In this paper, we first construct three aggregations schedules with ρ = 1 of latency 15R + Δ - 4, 2R + O(log R) + Δ and (1 + O(log R/3√R)) R + Δ respectively. Then, we obtain two aggregation schedules with ρ > 1 by expanding the first two aggregation schedules with ρ = 1. Both aggregation schedules with ρ > 1 have latency within constant factors of the minimum aggregation latency.

In this paper, we study the channel-aware minimum-latency broadcast scheduling problem using the probabilistic model. We establish an explicit relationship between the tolerated transmission-failure probability and the latency of the corresponding broadcast schedule. Such a tolerated transmission-failure probability is calculated in the strict sense that the failure to receive the message at any single node will lead to the entire broadcast failure and only if all nodes have successfully received the message, do we consider it a successful broadcast. We design a novel reconfigurable broadcast scheduling algorithm such that the latency is evaluated under such a strict definition of failure. Our derived latency bound associated with this new randomized algorithm is substantial to guarantee the low broadcast latency for the complete broadcasting success thereby.

In wireless ad hoc networks, greedy forward routing is a localized geographic routing algorithm in which one node discards a packet if none of its neighbors is closer to the destination of the packet than itself, or otherwise forwards the packet to the neighbor closest to the destination. If all nodes have the same transmission radii, the critical transmission radius for greedy forward routing is the smallest transmission radius which ensures packets can be delivered by greedy forward routing through any source-destination pair. In this paper, we study asymptotic critical transmission radii of randomly deployed wireless ad hoc networks. Assume network nodes are represented by a Poisson point process of density n over a unit-area convex compact region whose boundary curvature is bounded. We show that the ratio of critical transmission radii to radic (lnn/pin) is asymptotically almost surely equal to radic (1/ (2/3 - radic(3)/2pi)) ap 1.6.

Connected dominating set (CDS) has a wide range of applications in wireless ad hoc networks. A number of distributed algorithms for constructing a small CDS in wireless ad hoc networks have been proposed in the literature. The majority of these distributed algorithms follow a general two-phased approach. The first phase constructs a dominating set, and the second phase selects additional nodes to interconnect the nodes in the dominating set. In this paper, we prove that the approximation ratio of the two-phased algorithm in [10] is at most 7 1/3, improving upon the previous best-known approximation ratio of 7.6 due to [12]. We also propose a new two-phased approximation algorithm and prove that its approximation ratio is at most 6 7/18. Our analyses exploit an improved upper bound on the number independent points that can be packed in the neighborhood of a connected finite planar set.

Relative neighborhood graph (RNG) has been widely used in topology control and geographic routing in wireless ad hoc networks. Its maximum edge length is the minimum requirement on the maximum transmission radius by those applications of RNG. In this paper, we derive the precise asymptotic probability distribution of the maximum edge length of the RNG on a Poisson point process over a unit-area disk. Since the maximum RNG edge length is a lower bound on the critical transmission radius for greedy forward routing, our result also leads to an improved asymptotic almost sure lower bound on the critical transmission radius for greedy forward routing.

Broadcast is a fundamental operation in wireless networks and naive flooding is not practical because it cannot deal with interference. Scheduling is a good way to avoid interference, but previous studies on broadcast scheduling algorithms all assume highly theoretical models such as the unit disk graph model. In this work, we re-investigate this problem using the 2-disk and the signal-to-interference-plus-noise-ratio (SINR) model to realize it. We first design a constant approximation algorithm for the 2-disk model and then extend it to the SINR model. This result is the first result on broadcast scheduling algorithms in SINR model, to the best of our knowledge.

A wide range of applications for wireless ad hoc networks are time-critical and impose stringent requirement on the communication latency. This paper studies the problem Minimum-Latency Broadcast Scheduling (MLBS) in wireless ad hoc networks represented by unit-disk graphs. This problem is NP-hard. A trivial lower bound on the minimum broadcast latency is the radius R of the network with respect to the source of the broadcast, which is the maximum distance of all the nodes from the source of the broadcast. The previously best-known approximation algorithm for MLBS produces a broadcast schedule with latency at most 648 R. In this paper, we present three progressively improved approximation algorithms for MLBS. They produce broadcast schedules with latency at most 24 R -23, 16 R -15, and R + O (log R) respectively.

Data aggregation is a fundamental yet time-consuming task in wireless sensor networks. We focus on the latency part of data aggregation. Previously, the data aggregation algorithm of least latency [1] has a latency bound of (Delta - 1)R, where Delta is the maximum degree and R is the network radius. Since both Delta andRcould be of the same order of the network size, this algorithm can still have a rather high latency. In this paper, we designed an algorithm based on maximal independent sets which has an latency bound of 23R+ Delta - 18. Here Delta contributes to an additive factor instead of a multiplicative one; thus our algorithm is nearly constant approximation and it has a significantly less latency bound than earlier algorithms especially when Delta is large.

Flooding is one of the most fundamental operations in mobile ad hoc networks. Traditional implementation of flooding suffers from the problems of excessive redundancy of messages, resource contention, and signal collision. This causes high protocol overhead and interference with the existing traffic in the networks. Some efficient flooding algorithms were proposed to avoid these problems. However, these algorithms either perform poorly in reducing redundant transmissions or require each node to maintain 2-hop (or more) neighbors information. In the paper, we study the sufficient and necessary condition of 100 percent deliverability for flooding schemes that are based on only 1-hop neighbors information. We further propose an efficient flooding algorithm that achieves the local optimality in two senses: 1) the number of forwarding nodes in each step is minimal and 2) the time complexity for computing forwarding nodes is the lowest, which is O(nlogn), where n is the number of neighbors of a node. Extensive simulations have been conducted and simulation results have shown the excellent performance of our algorithm

In randomly-deployed wireless ad hoc networks with reliable nodes and links, vanishment of isolated nodes asymptotically implies connectivity of networks. However, in a realistic system, nodes may become inactive, and links may become down. The inactive nodes and down links cannot take part in routing/relaying and thus may affect the connectivity. In this paper, we study the connectivity of a wireless ad hoc network that is composed of unreliable nodes and links by investigating the distribution of the number of isolated nodes in the network. We assume that the wireless ad hoc network consists ofnnodes which are distributed independently and uniformly in a unit-area disk or square. Nodes are active independently with probability 0p1les1, and links are up independently with probability 0p2les1. A node is said to beisolatedif it doesn't have an up link to an active node. We show that if all nodes have a maximum transmission radiusrn=radiclnn+xi/pip1p2nfor some constant xi, then the total number of isolated nodes is asymptotically Poisson with meane-xiand the total number of isolated active nodes is also asymptotically Poisson with meanp1e-xi. In addition, the work can be extended for secure wireless networks which adoptm-composite key predistribution schemes in which a node is said to beisolatedif it doesn't have a secure link. Letpdenote the probability of the event that two neighbor nodes have a secure link. We show that if all nodes have a maximum transmission radiusrn=radiclnn+xi/pipnfor some constant xi, then the total number of isolated nodes is asymptotically Poisson with meane-xi.

Abstract—Flooding is one of the most fundamental operations in mobile ad hoc networks. Traditional implementation of flooding suffers from the problems of excessive redundancy of messages, resource contention, and signal collision. This causes high protocol overhead and interference to the existing traffic in the networks. Some efficient flooding algorithms were proposed to avoid these problems. However, these algorithms either perform poorly in reducing redundant transmissions, or require each node to maintain 2-hop (or more) neighbors information. In the paper, we study the sufficient and necessary condition of 100% deliverability for flooding schemes that are based on only 1-hop neighbors information. We further propose an efficient flooding algorithm that achieves the local optimality in two senses: 1) the number of forwarding nodes in each step is the minimal; 2) the time complexity for computing forwarding nodes is the lowest,

Greedy forward routing (abbreviated by GFR)in wireless ad hoc networks is a localized geographic routing in which each node discards a packet if one of its neighbors is closer to the destination of the packet than itself, or otherwise forwards the packet to the neighbor closest to the destination of the packet. If all nodes have the same transmission radii, the critical transmission radius for GFR is the smallest transmission radius which ensures that packets can be delivered between any source-destination pairs. In this paper, we study the asymptotic critical transmission radius for GFR in randomly deployed wireless ad hoc networks. We assume that the network nodes are represented by a Poisson point process of density n over a convex compact region of u it area with bounded curvature.Let ß0 = 1/ (⅔√3 over 2π) ≈ 1.62. We show that √ß0 1n n over πn is asymptotically almost surely (abbreviated by a.a.s.) the threshold of the critical transmission radius for GFR.I other words,for ß > ß0 if the trasmission radius is √ß 1n n over πn, it is a.a.s. packets can be delivered between any source-destination pairs; for any ß < ß0 if the transmission radius is √ß 1n noverπn, it is a.a.s. packets can't be delivered between some source-destination pair.

Nodes in wireless ad hoc networks may become inactive or unavailable due to, for example, internal breakdown or being in the sleeping state. The inactive nodes cannot take part in routing/relaying, and thus may affect the connectivity. A wireless ad hoc network containing inactive nodes is then said to be connected, if each inactive node is adjacent to at least one active node and all active nodes form a connected network. This paper is the first installment of our probabilistic study of the connectivity of wireless ad hoc networks containing inactive nodes. We assume that the wireless ad hoc network consists of n nodes which are distributed independently and uniformly in a unit-area disk, and are active (or available) independently with probability p for some constant 0

One of the main applications of wireless sensor networks is to provide proper coverage of their deployment regions. A wireless sensor network k-covers its deployment region if every point in its deployment region is within the coverage ranges of at least k sensors. In this paper, we assume that the sensors are deployed as either a Poisson point process or a uniform point process in a square or disk region, and study how the probability of the k-coverage changes with the sensing radius or the number of sensors. Our results take the complicated boundary effect into account, rather than avoiding it by assuming the toroidal metric as done in the literature.

This paper addresses the maximal lifetime scheduling for sensor surveillance systems with K sensors to 1 target. Given a set of sensors and targets in an Euclidean plane, a sensor can watch only one target at a time and a target should be watched by k, k \geq 1, sensors at any time. Our task is to schedule sensors to watch targets and pass data to the base station, such that the lifetime of the surveillance system is maximized, where the lifetime is the duration up to the time when there exists one target that cannot be watched by k sensors or data cannot be forwarded to the base station due to the depletion of energy of the sensor nodes. We propose an optimal solution to find the target watching schedule for sensors that achieves the maximal lifetime. Our solution consists of three steps: 1) computing the maximal lifetime of the surveillance system and a workload matrix by using linear programming techniques, 2) decomposing the workload matrix into a sequence of schedule matrices that can achieve the maximal lifetime, and 3) determining the sensor surveillance trees based on the above obtained schedule matrices, which specify the active sensors and the routes to pass sensed data to the base station. This is the first time in the literature that this scheduling problem of sensor surveillance systems has been formulated and the optimal solution has been found. We illustrate our optimal method by a numeric example and experiments in the end.

Abstract Conflict‐free channel assignment is a classic and fundamental problem in wirelessad hocnetworks. It seeks an assignment of the fewest channels to a given set of radio nodes with specified transmission ranges without causing either primary collision or secondary collision. It is NP‐hard even when all nodes are located in a plane and have the same transmission radii. We observe that a prior analysis of the approximation ratio of a classic greedy heuristic, FIRST‐FIT in smallest‐last ordering, is erroneous. In this paper, we provide a rigorous and tighter analysis of this heuristic and other greedy FIRST‐FIT heuristics. We obtain an upper bound of 13 on the approximation ratios of both FIRST‐FIT in smallest‐last ordering and FIRST‐FIT in radius‐decreasing ordering. Such upper bound can be reduced to 12 if all nodes have quasi‐uniform transmission radii. When all nodes have equal transmission radii, we obtain an upper bound of 7 on the approximation ratios of FIRST‐FIT in smallest‐last ordering, FIRST‐FIT in distance‐increasing ordering, and FIRST‐FIT in lexicographic ordering. In addition, for nodes with equal transmission radii, we present a spatial divide‐and‐conquer heuristic with approximation ratios of 12. All these heuristics, except FIRST‐FIT in smallest‐last ordering, are modified to heuristics for maximum independent set with the same approximation ratios. Copyright © 2006 John Wiley & Sons, Ltd.

The problem min-power k-connectivity seeks a power assignment to the nodes in a given wireless ad hoc network such that the produced network topology is k-connected and the total power is the lowest. In this paper, we present several approximation algorithms for this problem. Specifically, we propose a 3k-approximation algorithm for any k /spl ges/ 3, a (k + 12H (k))-approximation algorithm for k(2k - 1) /spl les/ n where n is the network size, a (k + 2 [(k + 1)/2])-approximation algorithm for 2 /spl les/ k /spl les/ 7, a 6-approximation algorithm for k = 3, and a 9-approximation algorithm for k = 4.

This paper addresses the maximal lifetime scheduling problem in sensor surveillance networks. Given a set of sensors and targets in a Euclidean plane, a sensor can watch only one target at a time, our task is to schedule sensors to watch targets, such that the lifetime of the surveillance system is maximized, where the lifetime is the duration that all targets are watched. We propose an optimal solution to find the target watching schedule for sensors that achieves the maximal lifetime. Our solution consists of three steps: 1) computing the maximal lifetime of the surveillance system and a workload matrix by using linear programming techniques; 2) decomposing the workload matrix into a sequence of schedule matrices that can achieve the maximal lifetime; 3) obtaining a target watching timetable for each sensor based on the schedule matrices. Simulations have been conducted to study the complexity of our proposed method and to compare with the performance of a greedy method.

One of the main applications of wireless sensor networks is to provide proper coverage of their deployment regions. A wireless sensor network k-covers its deployment region if every point in its deployment region is within the coverage ranges of at least k sensors. In this paper, we assume that the sensors are deployed as either a Poisson point process or a uniform point process in a square or disk region, and study how the probability of the k-coverage changes with the sensing radius or the number of sensors. Our results take the complicated boundary effect into account, rather than avoiding it by assuming the toroidal metric as done in the literature.

Wireless ad hoc networks with Bernoulli nodes provide a unified model of various important problems including fault-tolerance, randomized construction of virtual backbone, randomized broadcast routing, and randomized wake/sleep management. We assume that the wireless ad hoc network consists of n nodes which are distributed independently and uniformly in a unit-area disk and are active (or available) independently with some constant probability /spl rho/. Let /spl rho//sub n/ denote the random variable which is the smallest transmission range at which the active nodes form a connected network, and p/sub n/' denote the random variable which is the smallest transmission range at which the active nodes form a connected network and each inactive node is adjacent to at least one active node, /spl rho//sub n/ is referred to as the critical transmission range for connectivity of active modes, and /spl rho//sub n/' is referred to as the critical transmission range for connectivity of all nodes. In this paper, we derive the precise asymptotic distributions of /spl rho//sub n/ and /spl rho//sub n/'.

Abstract Since no fixed infrastructure and no centralized management present in wireless networks, a connected dominating set (CDS) of the graph representing the network is widely used as a virtual backbone. Constructing a minimum CDS is NP‐hard. In this paper, we propose a new greedy algorithm, called S‐MIS, with the help of Steiner tree that can construct a CDS within a factor of 4.8 + ln5 from the optimal solution. We also introduce the distributed version of this algorithm. We prove that the proposed algorithm is better than the current best performance ratio which is 6.8. A simulation is conducted to compare S‐MIS with its variation which is rS‐MIS. The simulation shows that the sizes of the CDSs generated by S‐MIS and rS‐MIS are almost the same. Copyright © 2005 John Wiley & Sons, Ltd.

In a typical mobile network, a group of channel sets identical the number of sectors in a cell is allocated to each cell type and reused symmetrically. Thus, deploying an underlay system requires costly modifications. A frequency allocation scheme called channel alternation and rotation for tiered wireless networks (CART) is proposed to exploit the scarce radio spectrum and current infrastructure build-outs. In CART, each cell type is allocated an extra channel set for rotating and alternating frequency channels among co-channel cells and between the two systems to enhance frequency reuse efficiency. In a typical environment requiring a carrier-to-interference ratio (C/I) about 17 dB, for example, CART increases offered traffic by 69 percent over a traditional two-tiered system. CART is simple and can also be easily modified for other wireless networks. Since infrastructure modification is not required, it incurs no additional costs.

We propose a new localized structure, namely, Incident MST and RNG Graph (IMRG), for topology control and broadcasting in wireless ad hoc networks. In the construction algorithm, each node first builds a modified relative neighborhood graph (RNG'), and then informs its one-hop neighbors its incident edges in RNG'. Each node then collects all its one-hop neighbors and the two-hop neighbors who have RNG edges to some of its one-hop neighbors, and builds an Euclidean minimum spanning tree of these nodes. Each node u keeps an edge uv only if uv is in the constructed minimum spanning tree. We analytically prove that the node degree of the IMRG is at most 6, it is connected and planar, and more importantly, the total edge length of the IMRG is within a constant factor of that of the minimum spanning tree. To the best of our knowledge, this is the first algorithm that can construct a structure with all these properties using small communication messages (at most 13n total messages, each with O(logn) bits) and small computation cost, where n is the number of wireless nodes. Test results are corroborated in the simulation study.

A range assignment to the nodes in a wireless ad hoc network induces a topology in which there is an edge between two nodes if and only if both of them are within each other’s transmission range. The critical transmission radius for kconnectivity is the smallest r such that if all nodes have the transmission radius r, the induced topology is k-connected. The critical neighbor number for k-connectivity is the smallest integer l such that if every node sets its transmission radius equal to the distance between itself and its l-th nearest neighbor, the induced topology is k-connected. In this paper, we study the asymptotic critical transmission radius for k-connectivity and asymptotic critical neighbor number for k-connectivity in a wireless ad hoc network whose nodes are uniformly and independently distributed in a unit-area square or disk. We provide a precise asymptotic distribution of the critical transmission radius for k-connectivity and an improved asymptotic almost sure upper bound on the critical neighbor number for k-connectivity.

Wieselthier et al. (2000) proposed three greedy heuristics for Min-Power Asymmetric Broadcast Routing: SPT (shortest-path tree), MST (minimum spanning tree), and BIP (broadcasting incremental power). Wan et al. (2001) proved that SPT has an approximation ratio of at least (n/2) where n is the total number of nodes, and both MST and BIP have constant approximation ratios. Based on the approach of pruning, Wieselthier et al. also proposed three greedy heuristics for Min-Power Asymmetric Multicast Routing: P-SPT (pruned shortest-path tree), P-MST (pruned minimum spanning tree), and P-BIP (pruned broadcasting incremental power). In this paper, we first prove that the approximation ratios of these three heuristics are at least (n-1/2),n-1, and n-2-o(1), respectively. We then present constant-approxiation algorithms for Min-Power Asymmetric Multicast Routing. We show that any /spl rho/-approximation Steiner tree algorithm gives rise to a c/spl rho/-approximation heuristic for Min-Power Asymmetric Multicast Routing, where c is a constant between 6 and 12. In particular, the Takahashi-Matsuyama Steiner tree heuristic leads to a heuristic called SPF (shortest-path first), which has an approximation ratio of at most 2c. We also present another heuristic, called MIPF (minimum incremental path first), for Min-Power Asymmetric Multicast Routing and show that its approximation ratio is between (13/3) and 2c. Both SPF and MIPF can be regarded as an adaptation of MST and BIP, respectively, in a different manner than pruning. Finally, we prove that any /spl rho/-approximation Steiner tree algorithm also gives rise to a 2/spl rho/-approximation algorithm for Min-Power Symmetric Multicast Routing.

Abstract We consider a large‐scale of wirelessad hocnetworks whose nodes are distributed randomly in a two‐dimensional region Ω (more specifically, a unit square). Givennwireless nodesV, each with transmission rangern, the wireless networks are often modeled by graphG(V,rn) in which two nodes are connected if and only if their Euclidean distance is no more thanrn. We first consider how to relate the transmission range with the number of nodes in a fixed area such that the resulted network can sustainkfault nodes in its neighborhood with high probability when all nodes have the same transmission range. We show that, for a unit‐area square region Ω, the probability that the networkG(V,rn) isk‐connected is at least${\rm e}^{-{\rm e}^{-\alpha}}$ when the transmission radiusrnsatisfies$n \pi r_n^2 \ge {\rm ln}\ n \,+ (2k - 3) {\rm ln}\, {\rm ln}\, n - 2 \,{\rm ln}(k - 1)! + 2 \alpha \ {\rm for} \, k >\,1$ andnsufficiently large. This result also applies to mobile networks when the moving of wireless nodes always generates randomly distributed positions. We also conduct extensive simulations to study the practical transmission range to achieve certain probability the network beingk‐connectivity, when the number of nodesnis not large enough. The relation between the minimum node degree and the connectivity of graphG(V,r) is also studied. Setting the transmission range of all nodes tornguarantees thek‐connectivity with high probability, but some nodes may have excessive number of neighbours in the graphG(V,rn). We then present a localized method to construct a subgraph of the network topologyG(V,rn) such that the resulting subgraph is stillk‐connected but with much fewer communication links maintained. We show that the constructed topology has onlyO(k · n) links and is a length spanner. Here a graphH ⊆ Gis spanner for graphG, if for any two nodes, the length of the shortest path connecting them inHis no more than a small constant factor of the length of the shortest path connecting them inG. Finally, we conduct some simulations to study the practical transmission range to achieve certain probability ofk‐connected whennis not large enough. Copyright © 2004 John Wiley & Sons, Ltd.

We consider a large-scale of wireless ad hoc networks whose nodes are distributed randomly in a two-dimensional region /spl Omega/. Given n wireless nodes V, each with transmission range r/sub n/, the wireless networks are often modeled by graph G(V, r/sub n/) in which two nodes are connected if their Euclidean distance is no more than r/sub n/. We show that, for a unit-area square region /spl Omega/, the probability G(V, r/sub n/) being k-connected is at least (e/sup -e/)/sup -/spl sigma// when n/spl pi/(r/sup 2/)/sub n/ /spl ges/ ln n + (2k - 3) ln ln n - 2 ln (k - 1)! + 2/spl sigma/ for k > 1 and n sufficiently large. This result also applies to mobile networks when the moving of wireless nodes always generates randomly and uniformly distributed positions. We also conduct extensive simulations to study the practical transmission range to achieve certain probability of k-connectivity when n is not large enough. The relation between the minimum node degree and the connectivity of graph G(V, r) is also studied.

A set S is dominating if each node in the graph G = (V, E) is either in S or adjacent to at least one of the nodes in S. The subgraph weakly induced by S is the graph G' = (V, E') such that each edge in E' has at least one end point in S. The set S is a weakly-connected dominating set (WCDS) of G if S is dominating and G' is connected G' is a sparse spanner if it has linear edges. In this paper, we present two distributed algorithms for finding a WCDS in O(n) time. The first algorithm has an approximation ratio of 5, and requires O(n log n) messages. The second algorithm has a larger approximation ratio, but it requires only O(n) messages. The graph G' generated by the second algorithm forms a sparse spanner with a topological dilation of 3, and a geometric dilation of 6.

This paper investigate fault tolerance for wireless ad hoc networks. We consider a large-scale of wireless networks whose nodes are distributed randomly in a unit-area square region. Given n wireless nodes V, each with transmission range rn, the wireless networks are often modeled by graph G(V,rn) in which two nodes are connected if their Euclidean distance is no more than rn.We first consider how the transmission range is related with the number of nodes in a fixed area such that the resulted network can sustain k fault nodes with high probability. We show that, for a unit-area square region, the probability that the network G(V,rn) is (k+1)-connected is at least e-e-α when the transmission radius rn satisfies n π rn2 ≥ ln n + (2k-1) ln ln n -2ln k! + 2α for k>0 and n sufficiently large. This result also applies to mobile networks when the moving of wireless nodes always generates randomly distributed positions. Our simulations show that n should be larger than 500 if k=2 or 3 and α = log n and n should be larger than 2500 if k=2 or 3 and α = log log n.We then present a localized method to control the network topology given a (k+1)-faults tolerant deployment G(V,rn) of wireless nodes such that the resulting topology is still (k+1)-faults tolerant but with O(kn) communication links maintained. We show that the constructed topology is also a length spanner. Here a subgraph H is spanner of graph G, if for any two nodes, the length of the shortest path connecting them in H is no more than a small constant factor of the length of the shortest path connecting them in G.Finally, we conduct some simulations to study the practical transmission range to achieve certain probability of k-connected when n is not large enough.

Nodes in wireless ad hoc networks may become inactive or unavailable due to, for example, internal breakdown or being in the sleeping state. The inactive nodes cannot take part in routing/relaying and thus may effect the connectivity. A wireless ad hoc network containing inactive nodes is then said to be connected if each inactive node is adjacent to at least one active node and all active nodes form a connected network. This paper is the first installment of our probabilistic study of the connectivity of wireless ad hoc networks containing inactive nodes. We assume that the wireless ad hoc network consists of n nodes, which are distributed independently and uniformly in a unit-area disk and are active (or available) independently with probability p for some constant 0 < p /spl les/ 1. We show that if all nodes have a maximum transmission radius r/sub n/ = /spl radic/(ln n+c//spl pi/pn) for some constant c, then the total number of isolated nodes is asymptotically Poisson with mean e/sup -c/ and the total number of isolated active nodes is also asymptotically Poisson with mean pe/sup -c/.

Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking. One of the fundamental problems in sensor networks is the calculation of the coverage. In Meguerdichian et al. (2001), it is assumed that the sensor has uniform sensing ability. We provide efficient distributed algorithms to optimally solve the best-coverage problem raised in the above-mentioned article. In addition, we consider a more general sensing model: the sensing ability diminishes as the distance increases. As energy conservation is a major concern in wireless (or sensor) networks, we also consider how to find an optimum best-coverage-path with the least energy consumption and how to find an optimum best-coverage-path that travels a small distance. In addition, we justify the correctness of the method proposed above that uses the Delaunay triangulation to solve the best coverage problem and show that the search space of the best coverage problem can be confined to the relative neighborhood graph, which can be constructed locally.

We propose a new geometric spanner for static wireless ad hoc networks, which can be constructed efficiently in a localized manner. It integrates the connected dominating set and the local Delaunay graph to form a backbone of the wireless network. Priori arts showed that both structures can be constructed locally with bounded communication costs. This new spanner has these following attractive properties: 1) the backbone is a planar graph, 2) the node degree of the backbone is bounded from above by a positive constant, 3) it is a spanner for both hops and length, 4) it can be constructed locally and is easy to maintain when the nodes move around, and 5) moreover, the communication cost of each node is bounded by a constant. Simulation results are also presented for studying its practical performance.

Several localized routing protocols guarantee the delivery of the packets when the underlying network topology is a planar graph. Typically, relative neighborhood graph (RING) or Gabriel graph (GG) is used as such planar structure. However, it is well-known that the spanning ratios of these two graphs are not bounded by any constant (even for uniform randomly distributed points). Bose et al. (1999) recently developed a localized routing protocol that guarantees that the distance traveled by the packets is within a constant factor of the minimum if Delaunay triangulation of all wireless nodes is used, in addition, to guarantee the delivery of the packets. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we model the network as a unit-disk graph (UDG), in which a link uv exists only if the distance /spl par/uv/spl par/ is at most the maximum transmission range. In this paper, we present a novel localized networking protocol that constructs a planar 2 5-spanner of UDG, called the localized Delaunay triangulation (LDEL), as network topology. It contains all edges that are both in the unit-disk graph and the Delaunay triangulation of all nodes. The total communication cost of our networking protocol is O(n log n) bits, which is within a constant factor of the optimum to construct any structure in a distributed manner. Our experiments show that the delivery rates of some of the existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies. Our simulations also show that the traveled distance of the packets is significantly less when the FACE routing algorithm is applied on LDEL, rather than applied on GG.

Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking. One of the fundamental problems in sensor networks is the calculation of the coverage. In Meguerdichian et al. (2001), it is assumed that the sensor has uniform sensing ability. In this paper, we give efficient distributed algorithms to optimally solve the best-coverage problem raised in Meguerdichian. Here, we consider the sensing model: the sensing ability diminishes as the distance increases. As energy conservation is a major concern in wireless (or sensor) networks, we also consider how to find an optimum best-coverage-path with the least energy consumption. We also consider how to find an optimum best-coverage-path that travels a small distance. In addition, we justify the correctness of the method proposed in Meguerdichian, that uses the Delaunay triangulation to solve the best coverage problem. Moreover, we show that the search space of the best coverage problem can be confined to the relative neighborhood graph, which can be constructed locally.

Several localized routing protocols (see Bose, P. and Morin, P., Proc. 10th Annual Int. Symp. on Algorithms and Computation ISAAC, 1999) guarantee the delivery of packets when the underlying network topology is the Delaunay triangulation of all wireless nodes. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we more accurately model the network as a unit-disk graph, UDG, in which a link between two nodes exists only if the distance between them is at most the maximum transmission range. Given a graph H, a spanning subgraph G of H is a t-spanner if the length of the shortest path connecting any two points in G is no more than t times the length of the shortest path connecting the two points in H. We present a novel localized networking protocol that constructs a planar 2.5-spanner of UDG, called the localized Delaunay triangulation, as network topology. It contains all edges that are in both the UDG and the Delaunay triangulation of all wireless nodes. Our experiments show that the delivery rates of existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies. The total communication cost of our networking protocol is O(n log n) bits. Moreover, the computation cost of each node u is O(d/sub u/ log d/sub u/), where d/sub u/ is the number of 1-hop neighbors of u in UDG.

The connected dominating set (CDS) has been proposed as the virtual backbone or spine of a wireless ad hoc network. Three distributed approximation algorithms have been proposed in the literature for minimum CDS. We first reinvestigate their performances. None of these algorithms have constant approximation factors. Thus these algorithms can not guarantee to generate a CDS of small size. Their message complexities can be as high as O(n/sup 2/), and their time complexities may also be as large as O(n/sup 2/) and O(n/sup 3/). We then present our own distributed algorithm that outperforms the existing algorithms. This algorithm has an approximation factor of at most 8, O(n) time complexity and O(n log n) message complexity. By establishing the /spl Omega/(n log n) lower bound on the message complexity of any distributed algorithm for nontrivial CDS, our algorithm is thus message-optimal.

A connected dominating set (CDS) for a graph G(V,E) is a subset V1 of V, such that each node in V--V1 is adjacent to some node in V1, and V1 induces a connected subgraph. A CDS has been proposed as a virtual backbone for routing in wireless ad hoc networks. However, it is NP-hard to find a minimum connected dominating set (MCDS). Approximation algorithms for MCDS have been proposed in the literature. Most of these algorithms suffer from a very poor approximation ratio, and from high time complexity and message complexity. Recently, new distributed heuristics for constructing a CDS were developed, with constant approximation ratio of 8. These new heuristics are based on a construction of a spanning tree, which makes it very costly in terms of communication overhead to maintain the CDS in the case of mobility and topology changes.In this paper, we propose the first distributed approximation algorithm to construct a MCDS for the unit-disk-graph with a emph constant approximation ratio, and emph linear time and emph linear message complexity. This algorithm is fully localized, and does not depend on the spanning tree. Thus, the maintenance of the CDS after changes of topology guarantees the maintenance of the same approximation ratio. In this algorithm each node requires knowledge of its single-hop neighbors, and only a constant number of two-hop and three-hop neighbors. The message length is O( log n) bits.

Automatic ring protection provides simple and rapid fault protection and restoration in telecommunication networks. To implement the automatic ring protection in general wavelength-division multiplexing (WDM) optical networks, the lightpaths are partitioned into groups each of which can be carried in a simple cycle of the underlying network. As the electronic line terminals are the dominant cost factor in the deployment of WDM optical networks, we study how to generate these partitions with minimum electronic line terminals. This optimization problem is NP-hard. We develop two polynomial-time approximation algorithms, with performance guarantees between 1.5 and 1.6 and between 1.5 and 1.5 + /spl epsi/, respectively. The second algorithm can be adapted, with the same performance guarantees, to the problem in which lightpaths are not prespecified and only the endpoints of each connection are given. Both algorithms can be easily adapted, with the same performance guarantees, to the problem in which only link protection is desired, and each group must be carried in a closed trail. The first algorithm matches and the second algorithm improves the approximation ratio obtained independently by Eilam et al. (see 14th Int. Symp. Distributed Computing, 2000).

Due to the limited resources available in the wireless ad hoc networking nodes, the scalability is crucial for network operations. One effective approach is to maintain only a sparse spanner of a linear number of links while still preseving the power-efficient route for any pair of nodes. For any spanner G, its power stretch factor is defined as the maximum ratio of the minimum power needed to support any link in this spanner to the least necessary. In this paper, we first consider several well-known proximity graphs including the relative neighborhood graph, Gabriel graph and Yao graph. These graphs are sparse and can be constructed locally in an efficient way. We show that the power stretch factor of the Gabriel graph is always one, and the power stretch factor of the Yao graph is bounded by a constant while the power stretch factor of the relative neighborhood graph could be as large as the network size minus one. Notice that all of these graphs do not have constant degrees. We further propose another sparse spanner that has both constant degree and constant power stretch factor. An efficient local algorithm is presented for the construction of this spanner.

Energy conservation is a critical issue in ad hoc wireless networks for node and network life, as the nodes are powered by batteries only. One major approach for energy conservation is to route a communication session along the routes which requires the lowest total energy consumption. This optimization problem is referred to as minimum-energy routing. While minimum-energy unicast routing can be solved in polynomial time by shortest-path algorithms, it remains open whether minimum-energy broadcast routing can be solved in polynomial time, despite the NP-hardness of its general graph version. Previously three greedy heuristics were proposed in Wieselthier et al. (2000): MST (minimum spanning tree), SPT (shortest-path tree), and BIP (broadcasting incremental power). They have been evaluated through simulations in Wieselthier et al.], but little is known about their analytical performance. The main contribution of this paper is the quantitative characterization of their performances in terms of approximation ratios. By exploring geometric structures of Euclidean MSTs, we have been able to prove that the approximation ratio of MST is between 6 and 12, and the approximation ratio of BIP is between /sup 13///sub 3/ and 12. On the other hand, the approximation ratio of SPT is shown to be at least /sup n///sub 2/, where n is the number of receiving nodes. To our best knowledge, these are the first analytical results for minimum-energy broadcasting.

SONET (Synchronous Optical NETworks) add-drop multiplexers (ADMs) are the dominant cost factor in the WDM(Wavelength Division Multiplexing)/SONET rings. The number of SONET ADMs required by a set of traffic streams is determined by the routing and wavelength assignment of the traffic streams. Previous works took as input the traffic streams with routings given a priori and developed various heuristics for wavelength assignment to minimize the SONET ADM costs. However, little was known about the performance guarantees of these heuristics. This paper contributes mainly in two aspects. First, in addition to the traffic streams with pre-specified routing, this paper also studies minimizing the ADM requirement by traffic streams without given routings, a problem which is shown to be NP-hard. Several heuristics for integrated routing and wavelength assignment are proposed to minimize the SONET ADM costs. Second, the approximation ratios of those heuristics for wavelength assignment only and those heuristics for integrated routing and wavelength assignment are analyzed. The new Preprocessed Iterative Matching heuristic has the best approximation ratio: at most 3/2.

Given a set of wireless network nodes N, the directed weighted transmission graph Gt has an edge uv if and only if node v is in the transmission range of node u and the weight of uv is typically defined as |uv| α + c for a real constant 2 ≤ α≤4 and c & 0. The minimum power topology Gm is the smallest subgraph of Gt that contains the shortest paths between all pairs of nodes. We described a distributed position-based networking protocol to construct the enclosure graph Ge, which is an approximation of Gm. The total communication complexity is O(n). Let dG(u) be the degree of node u in a graph G. The time complexity of each node u is O (dGt)). The space required at each node is O(dGt (u. This improves the previous result that approximates GmO(dGt(u)3) time using O(dGt(u2) spaces. We also show that the average degree dGe (u) is usually a constant, which is at most 6. Our result is first developed for stationary network and then extended to mobile network.

Due to discrete reuse cluster sizes, disjoined and uniformed channel assignment, conventional tri-sectored cellular systems have not taken full advantage of antenna directivities. We present a novel channel alternation and rotation (CAR) scheme to coordinate channel assignment with antenna directivities. In CAR, the cell layout is based on two-tier cell-reuse structure and each cell is allocated one extra channel set for channel alternations and rotations. The extra channel set gives the network designer the flexibility to assign channels according to nearest front lobe interference avoidant strategy to enhance co-channel interference ratio (C/I). CAR allows deployment of smaller, non-integer reuse cluster sizes based on C/I requirements, thus increases frequency reuse efficiency. CAR reuse plans can increase the channel capacity up to 31.25% while still maintain comparable C/I margins. CAR is simple and can be employed in any existing directional antenna system. Therefore, it truly does not impose any additional cost.

SONET/WDM networks using wavelength add—drop multiplexing can be constructed using certain graph decompositions used to form a “grooming,” consisting of unions of certain primitive rings. The existence of such decompositions when every pair of sites employs no more than ⅛ of the wavelength capacity is determined, with few possible exceptions, when the ring size is a multiple of four. The techniques developed rely heavily on tools from combinatorial design theory. © 2001 John Wiley & Sons, Inc.

Minimizing SONET ADM costs in single-hub SONET/WDM ring networks via traffic grooming has been discussed in a number of previous works. Previous work gives the exact minimum costs of uniform traffic in both unidirectional path-switched ring (UPSR) and two-fiber bidirectional line-switched ring (BLSR/2) and proves that the BLSR/2 would never be more expensive than UPSR under any traffic pattern, if all wavelengths have the same capacity. We consider how to groom both uniform and non-uniform traffic to minimize the cost of ADMs in the single-hub UPSR and BLSR/2 with mixed line speeds. We especially explore the grooming of traffic when wavelengths have two different capacities g/sub 1/=1 and g/sub 2/=4. We show that the problem can be confined to just consider the traffic request r/sub i//spl les/4 for all non-hub nodes i. By adopting the same cost model of Gerstel, Lin and Sasaki (see Proc. IEEE Infocom 99), i.e., ADMs with speed g/sub 1/=1 and g/sub 2/=4 cost 1 and 2.5 respectively, we provide optimal traffic partition and grooming for uniform traffic demands, and develop optimal or suboptimal solutions for non-uniform traffic demands, depending on the range of all demands from non-hub nodes.

We study wavelength assignment for lightpaths over WDM rings to minimize the SONET ADMs (add/drop multiplexers) used. This problem has attracted much attention recently. However, its computational complexity remains unknown, and the only known heuristic (Gerstel et al., 1998) which does not allow the splitting of lightpaths is problematic in terms of both the algorithm itself and its performance analysis. We first prove the NP-completeness of this problem, followed by a nontrivial randomized (3+e)/(1+e)-approximation scheme. We then present a tighter lower bound on the minimum number of ADMs required. After that, we show the incorrectness of the known heuristic and then modify it to make it correct. We also propose three additional heuristics. Their performances are compared through extensive simulation studies.

The growing interest in wireless systems and networks has led to the first wireless LAN (WLAN) protocols. The medium access control (MAC) layer protocols of such protocol suites are of key importance. The Radio Equipment and Systems (RES) Technical Committee of the European Telecommunications Standards Institute has proposed the high PErformance radio LAN (HIPERLAN) protocol suite. We present, study, analyze and evaluate the performance of the channel access control layer (lower sublayer of the MAC layer) of the HIPERLAN protocol suite for real-time traffic numerical results from both analysis and simulation are presented, so that the issues involved are better understood.

In SONET/WDM networks, one fiber supports multiple wavelengths and each wavelength supports several low rate tributary streams. Traffic grooming is then defined as properly using the SONET add/drop multiplexer (ADM) to electronically multiplex and demultiplex required tributary traffic patterns with minimal resource cost (wavelengths and ADMs). This paper studies the traffic grooming problem in single hub SONET/WDM networks and extends existing results. We analyze the real deployments, generalize their results, and study the practical special cases. We prove that BLSR/2 would never be more expensive than UPSR under any traffic pattern. We present the exact minimum costs of uniform traffic in both UPSR and BLSR/2. We also give approximation algorithms for optimal grooming of non-uniform traffic after showing that this problem is NP-complete. Finally, we consider how to select the line speeds if there are two different line speeds available.

SONET add-drop multiplexers (ADMs) are the dominant cost factor in the SONET/WDM rings. They can potentially be reduced by optical bypass via optical add-drop multiplexers (OADMs) and traffic grooming. In this paper we study the grooming of arbitrary traffic in WDM bidirectional line-switched rings (BLSRs) so as to minimize the ADM cost. Two versions of the minimum ADM cost problem are addressed. In the first version, each traffic stream has a predetermined routing. In the second version, the routing of each traffic stream is not given in advance; however, each traffic stream is fully duplex with symmetric demands, which must be routed along the same path but in opposite directions. In both versions, we further consider two variants depending on whether a traffic stream is allowed to be split at intermediate nodes. All the four combinations are NP-hard even for any fixed line-speed. General lower bounds on the minimum ADM cost are provided. Our traffic grooming follows a two-phased approach. The problem targeted at in each phase is NP-hard itself, except the second phase when the line speed is two. Various approximation algorithms are proposed in both phases, and their approximation ratios are analyzed.

Load-balanced routing in SONET rings has attracted much attention recently. Most prior works modeled the SONET rings as undirected rings and the traffic as undirected chords. While this model fits well to the traditional telephony applications, it is inefficient for the explosive Internet traffic and multimedia data communications, which exhibit an unidirectional and asymmetric nature. For these applications, it is proper to model the SONET rings as a pair of counter rotated rings and the traffic as directed chords. In this paper, we first explore general flow properties in counter rotated rings and then introduce flow rounding and unsplitting techniques. Afterward, an optimal integral routing algorithm is provided. Finally, we show the NP-completeness of optimal unsplit routing and present several polynomial-time approximation algorithms. © 2000 John Wiley & Sons, Inc.

In wavelength-routed optical networks, wavelength converters can potentially reduce the requirement on the number of wavelengths. The problem of placing a minimum number of wavelength converters in a WDM network so that any routing can be satisfied using no more wavelengths than if there were wavelength converters at every node was raised in Wilfong et al. (1998) and shown to be NP-complete in general WDM networks. Recently, it was proved in Kleinberg et al. (1999) that this problem is as hard as the well-known minimum vertex cover problem. In this paper, we further their study in two topologies that are of more practical concrete relevance to the telecommunications industry: trees and tree of rings. We show that the optimal wavelength converter placement problem in these two practical topologies are tractable. Efficient polynomial-time algorithms are presented.

In this paper we consider WDM networks with a tunable transmitter and a fixed-wavelength receiver at each station (similar results hold when the transmitter is fixed and the receiver is tunable). Traditionally, each station is required to be able to access all wavelength channels used in the network. Such requirement limits the number of wavelengths that can be exploited in a WDM network up to the size of the resolvable wavelength set of optical transceivers, which is very limited with current technology. In this paper we observe that this requirement is actually an overkill. To realize a communication topology, physical or logical, it is sufficient that the tunable range of the transmitter at each station covers all the wavelengths of the receivers at its neighboring stations. This observation leads to the study of optimal wavelength assignment to minimize the tunability requirement while still guaranteeing that each receiver has a unique wavelength channel. This optimization problem is shown to NP-complete in general and approximation algorithms with provable performance guarantees are presented. When the communication topologies are complete graphs, de Bruijin digraphs, Kautz digraphs, shuffle or rings, the optimal solutions are provided. Finally, we present tight lower bounds when the communication topology is a hypercube.

Load-balanced routing in SONET rings has attracted much attention recently. Most prior works model the SONET rings as undirected rings and the traffic as undirected chords. While this model fits well to the traditional telephony applications, it is inefficient for the explosive Internet traffic and multimedia data communications, which exhibit unidirectional and asymmetric nature. For these applications, it is proper to model the SONET rings as a pair of counter-rotated rings and the traffic as directed chords. In this paper we first explore general flow properties in counter-rotated rings, and then introduce flow rounding and unsplitting techniques. Afterwards an optimal integral routing algorithm is provided. Finally, we show the NP-completeness of optimal unsplit routing, and present several polynomial-time approximation algorithms.

The growing interest in wireless systems and networks has led to the first wireless LAN (WLAN) protocols. The medium access control (MAC) layer protocols of such protocol suites are of key importance. The Radio Equipment and Systems (RES) Technical Committee of the European Telecommunications Standards Institute has proposed the High PErformance Radio LAN (HIPERLAN) protocol suite. We present study, analyze and evaluate the performance of the MAC layer of the HIPERLAN protocol suite for asynchronous data transfer. Analytical models that take into account the phenomena of hidden nodes and capture are presented during the analysis. Numerical results from both analysis and simulation are presented, so that the issues involved are better understood.

Traditionally the routing in passive optical networks is based on an embedded regular virtual topology. However one important fact that has been neglected in the past is that the wavelength assignment to transceivers actually creates additional (logical) links not present in the virtual topology. Such side effect can be utilized to significantly reduce the number of hops between a pair of stations. This observation leads to the concept of super topology. This paper considers the hypercube as the embedded virtual topology. The ideas contained here are easily applicable to networks employing other virtual topologies as well. We present the structure of the super topology, the optimal routing algorithm, the distance between any pair of stations and the diameter in the super topology.

The time and wavelength division multiplexed (TWDM) access protocol is one of the most promising ways to exploit the enormous bandwidth in a single-mode optical fiber. We focus on constructing scalable TWDM networks based on rotator digraphs. To make the network be more economically and technically feasible and to improve the network performance, each station is equipped with multiple fixed transmitters and multiple fixed receivers. For such a network architecture, we present the optimal wavelength assignment and transmission schedule. We also study the cost performance relation and provide a scheme to support a large network site with multiple passive star couplers.

The single star optical network is limited in size by the available power budget. When the network size exceeds the number of connections a star coupler can support, it becomes necessary to use multiple passive star couplers to implement the network. The cost of a multi star optical network is determined by the number of fiber connections per station and the number of star couplers in the network. To reduce the cost of the network, it is desirable to use as least amount of fiber connections per station and star couplers as possible. We consider two multi star implementations of single hop networks, and discuss how to implement them with least cost.

This study investigates real-time checkpointing techniques in the context of distributed process control applications where checkpointing and recovery operations must meet timing constraints, such as process deadline and plant state validity. We introduce the notion of quasidurability, which allows one to make tradeoffs between storage device reliability and the process control and recovery timing constraints. Based on this notion, we study three protocols for real-time quasi-durable checkpointing and recovery. For each protocol, we analyze its recoverability and provide the sufficient and necessary conditions for a set of devices to be feasible for checkpointing and recovery.

Lightwave networks can be built by embedding virtual topologies over physical topologies. The optical passive star enables such embeddings easily. The Shuffle-net and the De-Bruijn graph are two popular virtual topologies proposed in the past for lightwave networks. Both however suffer from a lack of flexibility in scaling network sizes. We present a generalization of the De-Bruijn network which overcomes the limitation of the strict relationships between the network size parameters seen in the Shuffle-net and the De-Bruijn networks. A generalization for the Shuffle-net is also possible with this idea. We emphasize the support of time and wavelength division multiplexed media access protocols for such architectures and present several properties of the proposed network with respect to the same.

Time and wavelength division multiplexing (TWDM) has been shown to be one of the most promising ways to exploit the enormous bandwidth of single mode optical fiber. Lightwave networks employing TWDM are commonly based on optical passive star couplers. To overcome some existing technology constraints, a general hardware configuration that each station uses multiple fixed transmitters and fixed receivers is proposed. The maximal concurrency that can be possibly achieved by the TWDM single-hop lightwave networks with such general configuration is studied.