Seeding conflict in online society is a public issue obtaining increasing attention. In this paper, we take a step to study the problem of maximizing conflict in online social networks from the adversarial perspective. More specifically, we combine the widely used stochastic information propagation model and opinion dynamics model to jointly model the processes of adversarial content propagation and opinion evolution through peer pressure on social networks, based on which we define the adversarial perturbations maximization (APM) problem. The APM problem focuses on two popular network conflict measures, disagreement and polarization. Our analysis begins by showing the complex nature of the APM problem. We show that by decomposing the objective into a subtraction of two set functions, an upper bound of the objective which is essentially a difference of two submodular (DS) functions can be devised. Then inspired by the success of modular-modular procedure and reverse influence sampling technique in related optimization tasks, we build a two-level approximation framework to maximize the upper bound heuristically with a data-dependent guarantee and further strengthen the approximation result using the sandwich approximation framework. Also, we apply dimension reduction technique to design a faster naïve greedy algorithm for the objective. Experiments show both the seriousness of this problem and the performance of our proposed algorithms.

Consider a graph with nonnegative node weight. A vertex subset is called a CDS (connected dominating set) if every other node has at least one neighbor in the subset and the subset induces a connected subgraph. Furthermore, if every other node has at least m neighbors in the subset, then the node subset is called a [Formula: see text]CDS. The minimum-weight [Formula: see text]CDS problem aims at finding a [Formula: see text]CDS with minimum total node weight. In this paper, we present a new polynomial-time approximation algorithm for this problem, which improves previous ratio by a factor of 2/3. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This work was supported by the National Natural Science Foundation of China [Grant U20A2068] and the National Science Foundation [Grant III-1907472]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0306 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0306 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Theoretical studies on evolutionary algorithms have developed vigorously in recent years. Many such algorithms have theoretical guarantees in both running time and approximation ratio. Some approximation mechanism seems to be inherently embedded in many evolutionary algorithms. In this paper, we identify such a relation by proposing a unified analysis framework for a global simple multiobjective evolutionary algorithm (GSEMO) and apply it on a minimum weight general cover problem, which is general enough to subsume many important problems including the minimum submodular cover problem in which the submodular function is real-valued, and the minimum connected dominating set problem for which the potential function is nonsubmodular. We show that GSEMO yields theoretically guaranteed approximation ratios matching those achievable by a greedy algorithm in expected polynomial time when the potential function g is polynomial in the input size and the minimum gap between different g-values is a constant. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This work was supported by National Natural Science Foundation of China [11771013, U20A2068]; Zhejiang Provincial Natural Science Foundation of China [LD19A010001].

With the booming of Internet of Things (IoT), a content provider (CP) traditionally supported by the storage resources of a network service provider (NSP) can provide content services through the resources of IoT devices to significantly reduce the service latency. The CP, NSP, and IoT devices constitute an edge caching system, and it is crucial to efficiently utilize the storage resources in the system. Most existing studies ignore the idle storage resources of IoT devices. The few studies that consider the storage resources of IoT devices either are based on the assumption of complete information, or only utilize the storage resources of part of the IoT devices. In this article, we propose a contract theory and Stackelberg game-based storage resource allocation method to effectively utilize the storage resources in edge caching systems under information asymmetry. The interaction between the CP and the IoT is formalized as a contract design problem, and the interaction between the NSP and the CP is formulated as a two-stage Stackelberg game with a single leader and a single follower. We analyze the constraints in contract design and the Nash equilibrium of the Stackelberg game. We also propose a golden section search-based optimal contract design and pricing (GSSCP) algorithm to obtain the optimal contract of the CP and optimal price of the NSP storage resources. Simulation results demonstrate that the proposed method can make effective use of the storage resources and improve the CP utility in edge caching systems under information asymmetry.

Social media with online social networks has risen to be a prevalent force in information diffusion and public discourse. Despite its popularity and convenience, social media has been criticized for contributing to societal and ideological polarization as the result of trapping users in an echo chamber and filter bubbles. An emerging line of research focuses on ways to redesign content or link recommendation algorithms to mitigate the polarization phenomenon. However, existing works mainly concentrate on node-level balancing, while omitting the balancing effect that can be incurred by edge interaction in social networks. In this article, we take the first step to study the problem (CoAM) that assuming two campaigns are present in a network, how we should select seeds for each so as to maximize the interaction/activity between the followers of two campaigns (co-activity) after the diffusion process is finished. We begin our analysis by showing the hardness of CoAM under two diffusion models that are generalized from wildly used diffusion models and its objective function is neither submodular nor supermodular. This encourages us to design a submodular function that acts as a lower bound to the objective, by exploiting which we are able to devise a greedy algorithm with a provable approximation guarantee. To overcome the #P-hardness of diffusion calculation, we further extend the notion of random reverse-reachable (RR) set to devise a scalable instantiation of our approximation algorithm. We experimentally demonstrate the quality of our approximation algorithm on datasets collected from real-world social networks.

Mobile Crowdsourcing (MCS) is a novel distributed computing paradigm that recruits skilled workers to perform location-dependent tasks. A number of mature incentive mechanisms have been proposed to address the worker recruitment problem in MCS systems. However, most of them assume that there is a large enough worker pool and a sufficient number of users can be selected. This may be impossible in large-scale crowdsourcing environments. To address this challenge, we consider the MCS system defined on a location-aware social network provided by a social platform. In this system, we can recruit a small number of seed workers from the existing worker pool to spread the information of multiple tasks in the social network, thus attracting more users to perform tasks. In this paper, we propose a Multi-Task Diffusion Maximization (MT-DM) problem that aims to maximize the total utility of performing multiple crowdsourcing tasks under the budget. To accommodate multiple tasks diffusion over a social network, we create a multi-task diffusion model, and based on this model, we design an auction-based incentive mechanism, MT-DM-L. To deal with the high complexity of computing the multi-task diffusion, we adopt Multi-Task Reverse Reachable (MT-RR) sets to approximate the utility of information diffusion efficiently. Through both complete theoretical analysis and extensive simulations by using real-world datasets, we validate that our estimation for the spread of multi-task diffusion is accurate and the proposed mechanism achieves individual rationality, truthfulness, computational efficiency, and$(1-1/\sqrt{e}-\varepsilon )$approximation with at least$1-\delta$probability.

Influence Maximization (IM) is a well-known topic in mobile networks and social computing that aims to find a small subset of users that maximize the influence spread through an online information cascade. Recently, some cautious researchers have paid attention to the diversity of information dissemination, especially community-aware diversity, and formulated the diversified IM problem. Diversity is ubiquitous in many real-world applications, but these applications are all based on a given community structure. In social networks, we can form heterogeneous community structures for the same group of users according to different metrics. Therefore, how to quantify diversity based on multiple community structures is an interesting question. In this paper, we propose a Composite Community-Aware Diversified IM (CC-DIM) problem, which aims to select a seed set to maximize the influence spread and the composite diversity over all possible community structures under consideration. To address the NP-hardness of the CC-DIM problem, we adopt the technique of reverse influence sampling and design a random Generalized Reverse Reachable (G-RR) set to estimate the objective function. The composition of a random G-RR set is much more complex than the RR set used for the IM problem, which will lead to the inefficiency of traditional sampling-based approximation algorithms. Because of this, we further propose a two-stage algorithm, Generalized HIST (G-HIST). It can not only return a$(1-1/e-\varepsilon)$approximate solution with at least$(1-\delta)$probability but also improve the efficiency of sampling and ease the difficulty of searching by significantly reducing the average size of G-RR sets. Finally, we evaluate our proposed G-HIST on real datasets against existing algorithms. The experimental results show the effectiveness of our proposed algorithm and its superiority over other baseline algorithms.

The study focuses on achieving full view coverage in a camera sensor network to effectively monitor moving objects from multiple perspectives. Three key issues are addressed: camera direction selection, location selection, and moving object monitoring. There are three steps to maximize coverage of moving targets. The first step involves proposing the Maximum Group Set Coverage (MGSC) algorithm, which selects the camera sensor direction for traditional target coverage. In the second step, a composed target merged from a set of fixed directional targets represents multiple views of a moving object. Building upon the MGSC algorithm, the Maximum Group Set Coverage with Composed Targets (MGSC-CT) algorithm is presented to determine camera sensor directions that cover subsets of fixed directional targets. Additionally, a constraint on the number of cameras is imposed for camera location selection, leading to the study of the Maximum Group Set Coverage with Size Constraint (MGSC-SC) algorithm. Each of these steps formulates a problem on group set coverage and provides an algorithmic solution. Furthermore, improved versions of MGSC-CT and MGSC-SC are developed to enhance the coverage speed. Computer simulations are employed to demonstrate the significant performance of the algorithms.

Electric Vehicles (EVs) are becoming more and more popular in our daily life, which replaces traditional fuel vehicles to reduce carbon emissions and protect the environment. EVs need to be charged, but the number of charging piles in a Charging Station (CS) is limited, and charging is usually more time-consuming than fueling. According to this scenario, we propose a secure and efficient charging scheduling system based on a Directed Acyclic Graph (DAG)-blockchain and double-auction mechanism. In a smart area, it attempts to assign EVs to the available CSs in the light of their submitted charging requests and status information. First, we design a lightweight charging scheduling framework that integrates DAG-blockchain and modern cryptography technology to ensure security and scalability during performing scheduling and completing tradings. In this process, a constrained multi-item double-auction problem is formulated because of the limited charging resources in a CS, which motivates EVs and CSs in this area to participate in the market based on their preferences and statuses. Due to this constraint, our problem is more complicated and harder to achieve truthfulness as well as system efficiency compared to the existing double-auction model. To adapt to it, we propose two algorithms, namely, Truthful Mechanism for Charging (TMC) and Efficient Mechanism for Charging (EMC), to determine an assignment between EVs and CSs and pricing strategies. Then, both theoretical analysis and numerical simulations show the correctness and effectiveness of our proposed algorithms.

Emerging IoT applications have brought up new coverage problems with sink-based mobile sensors. In this paper, we first focus on the MinSum Sink-based Line Barrier Coverage (SLBC) problem of covering a line barrier with mobile sensors originated at sink stations distributed on the plane. The objective is to minimize the movement sum of the sensors for the sake of energy efficiency. When the sinks emit sensors with non-uniform radii, we prove the MinSum SLBC problem is$\mathcal{NP}$-complete via reducing from the Partition problem that is known$\mathcal{NP}$- complete. Then for the MinSum Sink-based on-a-Line Target Coverage (SLTC) problem of covering targets on a line, an exact algorithm is presented based on grouping the targets and transforming to the shortest path problem in the auxiliary graph induced by the vertices corresponding to the groups. The algorithm runs in time$O(n^{2})$when sinks emit sensors of uniform sensing radius, and in time$O(\vert R\vert ^{2}n^{2})$for sensors of non-uniform radii, where$n$and$\vert R\vert$are respectively the number of targets and different radii. Eventually for SLBC, we propose a pseudo additive fully polynomial-time approximation scheme by extending the algorithm for SLTC. The algorithm runs in$O(k^{2}(\frac{L}{\epsilon})^{2})$time and computes a coverage with total movement provably bounded by$opt+\epsilon$for any fixed sufficiently small$\epsilon > 0$, where$opt, k$and$L$are respectively the movement of an optimum solution, the number of sinks and the length of the barrier. At last, experiments are carried out to demonstrate the practical performance gain of our algorithms.

Given an element set E of order n, a collection of subsets [Formula: see text], a cost cSon each set [Formula: see text], a covering requirement refor each element [Formula: see text], and an integer k, the goal of a minimum partial set multicover problem (MinPSMC) is to find a subcollection [Formula: see text] to fully cover at least k elements such that the cost of [Formula: see text] is as small as possible and element e is fully covered by [Formula: see text] if it belongs to at least resets of [Formula: see text]. This problem generalizes the minimum k-union problem (MinkU) and is believed not to admit a subpolynomial approximation ratio. In this paper, we present a [Formula: see text]-approximation algorithm for MinPSMC, in which [Formula: see text] is the maximum size of a set in S. And when [Formula: see text], we present a bicriteria algorithm fully covering at least [Formula: see text] elements with approximation ratio [Formula: see text], where [Formula: see text] is a fixed number. These results are obtained by studying the minimum density subcollection problem with (or without) cardinality constraint, which might be of interest by itself.

Multidocument summarization problem deals with extracting main information and ideas from a set of related documents. Solution to this problem is to find an extraction strategy that aims at finding a small subset of sentences that is able to cover the most important information about the whole document set. Although a large number of machine-learning-based methods have shown great promise, the lack of high-quality training data poses an inherent obstacle to them. Furthermore, because of the proliferation of low-quality documents on the Internet, the existing summarization strategies, which are merely based on statistical features, get poor performance. In this article, we propose a new two-phase multidocument summarization strategy using content attention-based subtopic detection. First, inspired by distance dynamics-based community detection mechanism, we extract subtopics from the set of documents by having insight into their own content attention and also underlying semantic relations. Instead of complicated neural attention mechanisms, we propose a simple iteration-based content attention method to complete the subtopic detection task. Second, we formulate summarization from different subtopics as a combinatorial optimization problem of minimizing sentence distance and maximizing topic diversity. We prove the submodularity of the above optimization problem, which allows us to propose a new multidocument summarization algorithm based on the greedy mechanism. Finally, we experimentally validate our new algorithms on BBC news summary and wikiHow data. The results show our new algorithms outperform the state-of-the-art methods.

Blockchain can provide a dependable environment for the Internet of Things (IoT), while the high computing power and energy required by blockchain hinder its applications in IoT. Offloading the computation at the resource-limited IoT devices to a cloud/edge computing service provider (CESP) is a feasible solution to the execution of computation-intensive blockchain tasks. The CESP provides computing resources to IoT users with a cloud and multiple edge servers that work collaboratively such that the users are able to perform mobile blockchain services. Resource allocation and pricing of computing resources at the cloud/edges have a significant impact on the revenues of CESP and users. Most of the existing works on the cooperative edge-cloud for computation offloading assumes that a user is mapped to a prespecified edge server or the cloud. However, the CESP may choose a server from either the edge servers or the cloud to run the offloaded tasks by jointly considering the cost and income of the service provisioning. In this article, we formulate a Stackelberg game with CESP as the leader and users as the followers for cloud/edge computing resource management. We prove the existence of Stackelberg equilibrium and analyze the equilibrium. We then model the resource allocation and pricing at the CESP as a mixed-integer programming problem (MIP) with the objective to optimize the CESP's revenue and propose an efficient iterative greedy-and-search-based resource allocation and pricing algorithm (IGS). The algorithm solves two subproblems comprising the CESP's revenue optimization problem: resource allocation under a given resource price and resource pricing based on a specified resource allocation scheme. The first subproblem evaluates where to execute the computing tasks via a greedy-and-search-based approach, whereas the second subproblem estimates the resource price through golden section search. We conduct experiments through simulations. Simulation results show that the proposed algorithm can effectively improve the revenue of both the CESP and the IoT terminals.

Mobile edge computing system provides cloud computing capabilities at the edge of wireless mobile networks, ensuring low latency, highly efficient computing, and improved user experience. At the same time, computationally intensive components are offloaded from mobile devices to edge servers and distributed among the servers. Due to the special constraints (mobile devices' battery capacities, limited computing resources of one single edge server, inevitable edge server failure, etc.), there emerges a following problem. 1) How to guarantee the reliability of the offloaded computing? This problem brings in the following two other problems. 2) How to find the appropriate offloading point in the mobile program such that the computing tasks offloaded to cloud can be maximized, while the transmission energy consumption is minimized? 3) What is the achievable minimum latency tasks allocation strategy among multiple users' mobile devices and multiple edge servers? In this paper, we try to address the aforementioned problems. First, for the appropriate offloading point problem, we consider the offloading valuable basic constraint and propose a task merging strategy based on mobile program component call graphs to minimize the computational complexity of the program partition. Second, we formulate the second problem as a combinatorial optimization problem and transform it into an n-fold integer programming problem by mapping the remaining computing resources to a virtual component. Third, we design a reliable shadow component scheme between multilevel severs for the reliability problem. Finally, we develop a fast algorithm for the mix problem and analyze its performance and conduct experiments to prove the accuracy of our theoretical results.

With the explosive growth in the scale of cloud computing infrastructures, reliability and energy efficiency have become important concerns considering the great complexity of cloud data centers. There is an urgent need for efficient task assignment that can dispatch tasks to appropriate cloud data center servers, which is critical to achieve reliability and energy efficiency in current cloud data centers. Most of the research on task assignment focuses on only one of the objectives of reliability and energy efficiency, while the two objectives are intrinsically conflicting with each other. In this paper, we deal with the problem of task assignment in data centers, with the objective of minimizing the energy consumption while providing failure tolerance to task execution failure. We propose a reliability-aware and energy-efficient task replica assignment algorithm based on running task replicas at a low speed and enabling multiple task replicas to share the same server resources. Each task in a job processed by the cloud computing platform has two instances: main task and task replica (shadow). Each main task runs on an individual server, and the task replica associated with the main task is assigned on a different server. The main tasks run at the full server speed, while the task replicas run at a lower rate than the main tasks. The task replicas can be mapped onto dedicated backup servers or be assigned to the servers on which the main tasks are running. Multiple task replicas can share the same server resources to reduce the number of servers required. We conduct experiments through simulations. Experimental results demonstrate that the proposed algorithm can effectively reduce the energy consumption, while achieving a good balance between the number of servers used and job completion time.

As vehicles are becoming more and more intelligent, mobile data traffic in vehicular ad hoc network (VANET) has been increasing dramatically. This makes the communication capacity of VANET systems and the computing resources of vehicles insufficient. In the meantime, location-aware large-scale distributed services with very low latency and high reliability are demanded by most of the novel functions, such as accident alarming, and congestion warning, in the intelligent transportation system. To meet these claimed characteristics of VANET, we first present a novel architecture that integrates vehicular fog computing and vehicle-to-vehicle (V2V) communication technologies. Lower latency and higher quality services can be supplied to vehicles by nearby fog servers, which are virtualized from vehicles that locate close enough and communicate using the V2V link. However, like all collaborative systems, computing reliability is vital to collaborative VANET. In this article, we design a novel energy-efficient proactive replication mechanism. Follower vehicles calculate with a lazy rate act as backups of host vehicles to ensure the reliability of the system. Considering the time sensitivity of computing requirements in VANET, the upper bound on the total number of failures is proposed through theoretical analysis. Then, the lower bound on the lazy calculating rate of followers is derived by balancing the tradeoffs between delay and energy. A fast algorithm for searching this lower bound based on the discrete Newton method is also proposed. Results of numerical experiments show that our new mechanism is effective in energy saving and reliability enhancing.

MapReduce jobs need to shuffle a large amount of data over the network between mapper and reducer nodes. The shuffle time accounts for a big part of the total running time of the MapReduce jobs. Therefore, optimizing the makespan of shuffle phase can greatly improve the performance of MapReduce jobs. A large fraction of production jobs in data centers are recurring with predictable characteristics, and the recurring jobs split the network into periodic busy and idle time slots, which allows us to better schedule the shuffle data in order to reduce the makespan of shuffle phase with the future predictable network status available. In this paper, we formulate the shuffle scheduling problem with the aim to minimize the makespan of MapReduce shuffle phase by leveraging the predictable periodic network status. We then propose a simple yet effective network-aware shuffle scheduling algorithm (NAS) to reduce the number of idle time slots required to transfer the shuffle data so as to reduce the shuffle makespan. We also prove that the proposed algorithm NAS is a 3/2-approximation algorithm to the shuffle scheduling problem when all the future idle time slots have the same duration. We finally conduct experiments through simulations. Experimental results demonstrate the proposed algorithm can effectively reduce the makespan of MapReduce shuffle phase and increase network utilization.

Guiding users to actively expanding their online social circles is one of the primary strategies for enhancing user participation and growing online social networks. In this paper, we study the active friending problem which aims at providing users with the strategy for methodically sending invitations to successfully build a friendship with target users. We consider the prominent linear threshold model for the friending process and formulate the active friending problem as an optimization problem. The key observation is the relationship between the active friending problem and the minimum subset cover problem, based on which we present the first randomized algorithm with a data-independent approximation ratio and a controllable success probability for general graphs. The performance of the proposed algorithm is theoretically analyzed and supported by encouraging simulation results done on extensive datasets.

Motivated by the need for analyzing the rapidly producing data streams, such as images, videos, sensor data, etc, in a timely manner, the study on the streaming algorithms to extract representative information from massive data to maximize some objective function is therefore important and urgent. Most of previous works are assumed under a noise-free environment, while in many realistic applications obtaining the exact function value is hard or computing the function value may cost much, which brings the noisy version. Hence in this paper, we address a more general problem to select a subset of at most k elements from the stream to maximize a noisy set function (not necessarily submodular). To be specific, we cast our problem as the streaming submodular maximization problem under multiplicative and additive noise models. We develop an efficient thresholding streaming algorithm, which calls several copies of a subroutine in parallel. Therefore, this algorithm only requires two passes over data and has a memory independent of data size. For both of noisy models, its approximation guarantee approaches 2/k. In our numerical experiments, we extensively evaluate the effectiveness of our thresholding streaming algorithm on some applications in real data set.

Online misinformation has been considered as one of the top global risks as it may cause serious consequences such as economic damages and public panic. The misinformation prevention problem aims at generating a positive cascade with appropriate seed nodes in order to compete against the misinformation. In this paper, we study the misinformation prevention problem under the prominent independent cascade model. Due to the #P-hardness in computing influence, the core problem is to design effective sampling methods to estimate the function value. The main contribution of this paper is a novel sampling method. Different from the classic reverse sampling technique which treats all nodes equally and samples the node uniformly, the proposed method proceeds with a hybrid sampling process which is able to attach high weights to the users who are prone to be affected by the misinformation. Consequently, the new sampling method is more powerful in generating effective samples used for computing seed nodes for the positive cascade. Based on the new hybrid sample technique, we design an algorithm offering a (1-1/e-€)-approximation. We experimentally evaluate the proposed method on extensive datasets and show that it significantly outperforms the state-of-the-art solutions.

The widespread and effective online social networks may cause misinformation to diffuse in the networks, which could lead to public panic and even serious economic consequences. The classical misinformation containment (MC) problem aims to select a small node set as positive seeds to compete against the misinformation and limit the influence of misinformation as much as possible, where the misinformation seed set is given. Most of the prior works concentrate on either minimizing the number of users infected by misinformation or maximizing the number of users protected by the positive cascade. That is, they only concentrate on optimizing the number of nodes. However, the interaction effects between nodes differ from user to user and the related profit obtained from interaction activities may also be different. This article proposes a novel problem, called profit minimization of misinformation (PMM), which is the first to analyze the profit of activity in the MC problem. Given a misinformation seed set, the PMM problem aims at selecting a node set satisfying the cardinality constraint to minimize the profit of edges starting from infected nodes but ending at infected or protected nodes. Based on the sandwich method, we design a data-dependent approximation scheme for the PMM problem. We approximate the upper and lower bounds of the objective in the equivalent problem by the reverse influence sampling technique. Our algorithm is verified on realistic data sets, which demonstrate the superiority of our method.

In[1], the financial support information in the first footnote should have read as follows.

In the past decade, tremendous research effort has been devoted to viral marketing. Most existing works on seed selection in social networks do not take into account the scenario when a profit can be generated from group activities. Each activity has a profit that can be measured by the excitement of the participants. The excitement about one piece of information can vary significantly among different groups of people. Given a social network and a profit function, how can we select the seed users to maximize the expected total amount of profit? This problem is essentially different from the classic influence maximization problem, and existing approaches cannot be directly applied to solve the problem. In this paper, we study the problem of activity profit maximization in social networks. We first prove that the maximizing activity profit problem is nondeterministic polynomial time-hard and cannot be approximated within a constant factor by the simple greedy algorithm. Supermodular degree of a function measures the extent to which it violates submodularity. We design an algorithm that achieves an approximation ratio of (1/(Δ+ 2)) provided that the supermodular degree of the social graph is bounded with A. We then develop an exchange-based technique to further improve the quality of the solution. We also devise a randomized variation approach to overcome the computational burden of the proposed algorithms. Extensive experimental results on three real benchmark data sets demonstrate the efficacy and efficiency of our algorithms over several baseline heuristics.

The widespread online misinformation could cause public panic and serious economic damages. The misinformation containment problem aims at limiting the spread of misinformation in online social networks by launching competing campaigns. Motivated by realistic scenarios, we present the first analysis of the misinformation containment problem for the case when an arbitrary number of cascades are allowed. This paper makes four contributions. First, we provide a formal model for multi-cascade diffusion and introduce an important concept called as cascade priority. Second, we show that the misinformation containment problem cannot be approximated within a factor of $\Omega(2^{\log^{1-\epsilon}n^4})$ in polynomial time unless $NP \subseteq DTIME(n^{\polylog{n}})$. Third, we introduce several types of cascade priority that are frequently seen in real social networks. Finally, we design novel algorithms for solving the misinformation containment problem. The effectiveness of the proposed algorithm is supported by encouraging experimental results.

Finding a connected dominating set (CDS) in a given graph is a fundamental problem and has been studied intensively for a long time because of its application in computer science and operations research, e.g., connected facility location and wireless networks. In some cases, fault-tolerance is desirable. Taking wireless networks as an example, since wireless nodes may fail due to accidental damage or energy depletion, it is desirable that the virtual backbone has some fault-tolerance. Such a problem can be modeled as finding a minimum k-connected m-fold dominating set ((k, m)-CDS) of a graph G = (V, E), which is a node set D such that every node outside of D has at least m neighbors in D and the subgraph of G induced by D is k-connected. In this paper, we study the minimum weight (1, m)-CDS problem ((1, m)-MWCDS), and present an (H(δ + m) + 2H(δ − 1))-approximation algorithm, where δ is the maximum degree of the graph and H(·) is the Harmonic number. Notice that the state-of-the-art algorithm achieves O(l...

While the online social network (OSN) has brought much convenience to users, there are still some serious problems, such as personal privacy leaks. Today, OSN security and privacy protection are one of the most important focuses of the research. In this paper, we present an intelligent privacy protection approach to solve problems of security and privacy protection in OSNs. First, the proposed algorithm combines a neural network with a hybrid hierarchy genetic algorithm and radial basis function, which is used to construct a prediction model of OSN security. Then, a support vector machine is applied to preprocess information of the OSN, and the attribute-based encryption scheme is adopted to encrypt the OSN information. Finally, a particle swarm optimization algorithm is used to improve OSN security and privacy protection. The experimental results demonstrate the effectiveness of the proposed method.

Misinformation and rumor can spread rapidly and widely through online social networks and therefore rumor controlling has become a critical issue. It is assumed in the existing works that there is a single authority whose goal is to minimize the spread of rumor by generating a positive cascade. In this paper, we study a more realistic scenario when there is multiple positive cascades generated by different agents. For the multiple-cascade diffusion, we propose the peer-to-peer independent cascade model for private social communications. The main contribution of this paper is an analysis of the rumor blocking effect (i.e., the number of the users activated by rumor) when the agents noncooperatively generate the positive cascades. We show that the rumor blocking effect provided by the Nash equilibrium will not be arbitrarily worse even if the positive cascades are generated noncooperatively. In addition, we give a discussion on how the cascade priority and activation order affect the rumor blocking problem. We experimentally examine the Nash equilibrium of the proposed games by simulations done on real social network structures.

We study the problem of active friending in online social networks. Given an initiator who want to friend a target person on a social network, we propose a strategy to support active friending through a series of recommendation lists. The lists serve as a step-to-step guidance for the initiator. We formulate an optimization problem, Constrained Active Friending CAF), for configuring the recommendation lists in the active friending process. Our goal is to maximize the acceptance probability of the invitation from the initiator to the friending target, by recommending selective intermediate friends to approach the target. We prove that CAF problem is NP-hard under the linear threshold model. We propose an algorithm based on discrete super-differentials that derives a guaranteed approximation for this problem. Extensive evaluation results on benchmark social network datasets validate the effectiveness and efficiency of our algorithms.

Social networks allow rapid spread of ideas and innovations while the negative information can also propagate widely. When the cascades with different opinions reaching the same user, the cascade arriving first is the most likely to be taken by the user. Therefore, once misinformation or rumor is detected, a natural containment method is to introduce a positive cascade competing against the rumor. Given a budget k, the rumor blocking problem asks for k seed users to trigger the spread of the positive cascade such that the number of the users who are not influenced by rumor can be maximized. The prior works have shown that the rumor blocking problem can be approximated within a factor of (1 - 1/e- δ) by a classic greedy algorithm combined with Monte Carlo simulation with the running time of O(k3mn ln n/δ2), where n and m are the number of users and edges, respectively. Unfortunately, the Monte-Carlo-simulation-based methods are extremely time consuming and the existing algorithms either trade performance guarantees for practical efficiency or vice versa. In this paper, we present a randomized algorithm which runs in O(km ln n/δ2) expected time and provides a (1 - 1/e - δ)-approximation with a high probability. The experimentally results on both the real-world and synthetic social networks have shown that the proposed randomized rumor blocking algorithm is much more efficient than the state-of-the-art method and it is able to find the seed nodes which are effective in limiting the spread of rumor.

One model for viral marketing is the positive influence. In this model, an inactive node is changed into active if and only if at least half of its neighbors are already in active state. The positive influence model can be viewed as a special case of a general threshold model, in which the threshold function at each node has value one if at least a certain fraction of neighbors are in active state, and value 0 otherwise. This function can be proved to be monotonically increasing and nonsubmodular for any predefined fraction. Therefore, given a seed set, the number of influenced nodes is not submodular with respect to the size of the seed set. This fact makes those optimization problems related with positive influence very hard, including the minimum partial positive influence seeding problem: Given a social network G = (V, E) and a number 02H ([pn]))-approximation algorithm for the minimum partial positive influence seeding problem, where n is the number of nodes, and H(·) is the Harmonic number.

Taking the advantage of high-throughput single nucleotide polymorphism (SNP) genotyping technology, large genome-wide association studies (GWASs) have been considered to hold promise for unraveling complex relationships between genotypes and phenotypes. Current multi-locus-based methods are insufficient to detect interactions with diverse genetic effects on multifarious diseases. Also, statistic tests for high-order epistasis ( ≥ 2 SNPs) raise huge computational and analytical challenges because the computation increases exponentially as the growth of the cardinality of SNPs combinations. In this paper, we provide a simple, fast and powerful method, named DAM, using Bayesian inference to detect genome-wide multi-locus epistatic interactions in multiple diseases. Experimental results on simulated data demonstrate that our method is powerful and efficient. We also apply DAM on two GWAS datasets from WTCCC, i.e., Rheumatoid Arthritis and Type 1 Diabetes, and identify some novel findings. Therefore, we believe that our method is suitable and efficient for the full-scale analysis of multi-disease-related interactions in GWASs.

Wireless sensor networks (WSNs) have been widely used in a plenty of applications. To achieve higher efficiency for data collection, WSNs are often partitioned into several disjointed clusters, each with a representative cluster head in charge of the data gathering and routing process. Such a partition is balanced and effective, if the distance between each node and its cluster head can be bounded within a constant number of hops, and any two cluster heads are connected. Finding such a cluster partition with minimum number of clusters and connectors between cluster heads is defined as minimum connected d-hop dominating set (d-MCDS) problem, which is proved to be NP-complete. In this paper, we propose a distributed approximation named CS-Cluster to address the d-MCDS problem under unit disk graph. CS-Cluster constructs a sparser d-hop maximal independent set (d-MIS), connects the d-MIS, and finally checks and removes redundant nodes. We prove the approximation ratio of CS-Cluster is (2d + 1)λ, where λ is a parameter related with d but is no more than 18.4. Compared with the previous best result O(d2), our approximation ratio is a great improvement. Our evaluation results demonstrate the outstanding performance of our algorithm compared with previous works.

In a wireless sensor network, the virtual backbone plays an important role. Due to accidental damage or energy depletion, it is desirable that the virtual backbone is fault-tolerant. A fault-tolerant virtual backbone can be modeled as a k-connected m-fold dominating set ((k, m)-CDS for short). In this paper, we present a constant approximation algorithm for the minimum weight (k, m)-CDS problem in unit disk graphs under the assumption that k and m are two fixed constants with m ≥ k. Prior to this paper, constant approximation algorithms are known for k = 1 with weight and 2 ≤ k ≤ 3 without weight. Our result is the first constant approximation algorithm for the (k, m)-CDS problem with general k, m and with weight. The performance ratio is (α+5ρ) fork ≥ 3 and (α+2.5ρ) for k = 2, where α is the performance ratio for the minimum weight m-fold dominating set problem and ρ is the performance ratio for the subset k-connected subgraph problem (both problems are known to have constant performance ratios).

For the purpose of propagating information and ideas through a social network, a seeding strategy aims to find a small set of seed users that are able to maximize the spread of the influence, which is termed influence maximization problem. Despite a large number of works have studied this problem, the existing seeding strategies are limited to the models that cannot fully capture the characteristics of real-world social networks. In fact, due to high-speed data transmission and large population of participants, the diffusion processes in real-world social networks have many aspects of uncertainness. As shown in the experiments, when taking such uncertainness into account, the state-of-the-art seeding strategies are pessimistic as they fail to trace the influence diffusion. In this paper, we study the strategies that select seed users in an adaptive manner. We first formally model the dynamic independent Cascade model and introduce the concept of adaptive seeding strategy. Then, based on the proposed model, we show that a simple greedy adaptive seeding strategy finds an effective solution with a provable performance guarantee. Besides the greedy algorithm, an efficient heuristic algorithm is provided for better scalability. Extensive experiments have been performed on both the real-world networks and synthetic power-law networks. The results herein demonstrate the superiority of the adaptive seeding strategies to other baseline methods.

To save energy and alleviate interference, connected dominating set (CDS) was proposed to serve as a virtual backbone of wireless sensor networks (WSNs). Because sensor nodes may fail due to accidental damages or energy depletion, it is desirable to construct a fault tolerant virtual backbone with high redundancy in both coverage and connectivity. This can be modeled as a k-connected m-fold dominating set (abbreviated as (k, m)-CDS) problem. A node set C ⊆ V (G) is a (k, m)-CDS of graph G if every node in V(G)\C is adjacent with at least m nodes in C and the subgraph of G induced by C is k-connected. Constant approximation algorithm is known for (3, m)-CDS in unit disk graph, which models homogeneous WSNs. In this paper, we present the first performance guaranteed approximation algorithm for (3, m)-CDS in a heterogeneous WSN. In fact, our performance ratio is valid for any topology. The performance ratio is at most γ, where γ = α + 8 + 2 ln(2α - 6) for α ≥ 4 and γ = 3α +2 ln 2 for α <; 4, and α is the performance ratio for the minimum (2, m)-CDS problem. Using currently best known value of α, the performance ratio is ln δ +o(ln δ), where δ is the maximum degree of the graph, which is asymptotically best possible in view of the non-approximability of the problem. Applying our algorithm on a unit disk graph, the performance ratio is less than 27, improving previous ratio 62.3 by a large amount for the (3, m)-CDS problem on a unit disk graph.

Community detection aims to reveal the community structure in a social network, which is one of the fundamental problems. In this paper we investigate the community detection problem based on the concept of terminal set. A terminal set is a group of users within which any two users belong to different communities. Although the community detection is hard in general, the terminal set can be very helpful in designing effective community detection algorithms. We first present a 2-approximation algorithm running in polynomial time for the original community detection problem. In the other issue, in order to better support real applications we further consider the case when extra restrictions are imposed on feasible partitions. For such customized community detection problems, we provide two randomized algorithms which are able to find the optimal partition with a high probability. Demonstrated by the experiments performed on benchmark networks the proposed algorithms are able to produce high-quality communities.

Using a connected dominating set (CDS) to serve as a virtual backbone of a wireless sensor network is an effective way to save energy and alleviate broadcasting storm. Since nodes may fail due to accidental damage or energy depletion, it is desirable to construct a fault tolerant CDS, which can be modeled as a k-connected m-fold dominating set ((k, m)-CDS for short). A subset of nodes C ⊆ V(G) is a (k, m)-CDS of G if every node in V(G)\C is adjacent with at least m nodes in C and the subgraph of G induced by C is k-connected. In this paper, we present an approximation algorithm for the minimum (3, m)-CDS problem with m > 3, which has size at most γ times that of an optimal solution, where γ = α + 8 + 21n(2α - 6) for α > 4 and γ = 3α + 2 In 2 for α <; 4, and α is the approximation ratio for the minimum (2, m)-CDS problem. This is the first performance-guaranteed algorithm for the minimum (3, m)-CDS problem in a general wireless network, and improves previous performance ratio in a homogeneous wireless sensor network by a large amount.

In a social network, influence diffusion is the process of spreading innovations from user to user. An activation state identifies who are the active users who have adopted the target innovation. Given an activation state of a certain diffusion, effector detection aims to reveal the active users who are able to best explain the observed state. In this paper, we tackle the effector detection problem from two perspectives. The first approach is based on the influence distance that measures the chance that an active user can activate its neighbors. For a certain pair of users, the shorter the influence distance, the higher probability that one can activate the other. Given an activation state, the effectors are expected to have short influence distance to active users while long to inactive users. By this idea, we propose the influence-distance-based effector detection problem and provide a 3-approximation. Second, we address the effector detection problem by the maximum likelihood estimation (MLE) approach. We prove that the optimal MLE can be obtained in polynomial time for connected directed acyclic graphs. For general graphs, we first extract a directed acyclic subgraph that can well preserve the information in the original graph and then apply the MLE approach to the extracted subgraph to obtain the effectors. The effectiveness of our algorithms is experimentally verified via simulations on the real-world social network.

Energy efficiency is an important issue in the study of wireless sensor networks. Given a set of targets and a set of sensors with bounded lifetime, the maximum lifetime k-coverage problem is to schedule active/sleeping status of sensors to maximize the time period during which every target is covered by at least k active sensors. Previously, it was known that when the sensing ranges are uniform, this problem has a polynomial time (4+ε)-approximation for k = 1 and (6+ε)-approximation for k = 2. In this paper, we make significant progress by showing that for any positive integer k, there exists a polynomial-time (3 + ε)-approximation.

Wireless sensor networks (WSNs) have been widely used in plenty of applications. To achieve higher efficiency for data collection, WSNs are often partitioned into several disjointed clusters, each with a representative cluster head in charge of the data gathering and routing process. Such a partition is balanced and effective if the distance between each node and its cluster head can be bounded within a constant number of hops, and any two cluster heads are connected. Finding such a cluster partition with minimum number of clusters and connectors between cluster heads is defined as minimum connected d-hop dominating set (d-MCDS) problem, which is proved to be NP-complete. In this paper, we propose a distributed approximation algorithm, named CS-Cluster, to address the d-MCDS problem. CS-Cluster constructs a sparser d-hop maximal independent set (d-MIS), connects the d-MIS and finally checks and removes redundant nodes. We prove the approximation ratio of CS-Cluster is (2d + l)λ, where λ is a parameter related with d but is no more than 18.4. Compared with the previous best result O(d2), our approximation ratio is a great improvement. Our evaluation results demonstrate the outstanding performance of our algorithm compared with previous works.

Energy efficiency is an important issue in the study of wireless sensor networks. Given a homogeneous set of sensors with unit lifetime and a set of target points, find an active/sleeping schedule for sensors to maximize the lifetime of k-coverage, i.e., the time period during which every target point is covered by at least k active sensors. This is a well known problem in wireless sensor networks concerning with energy efficiency. When k = 1, it is called the maximum lifetime coverage problem which has been proved to have a polynomial-time (4 + ε)-approximation. When k ≥ 2, it is the maximum lifetime fault-tolerant coverage problem. Previous to this work, only in the case k = 2, a polynomial-time (6 + ε)-approximation is found. In this paper, we will make a significant progress by showing that for any positive integer k, there exists a polynomial-time (4 + ε)-approximation, and for k = 1,2, the performance ratio can be improved to (3 + ε).

A boy wants to make friends with a pretty girl. He feels that he may get rejected if he invites her directly. In this situation, what he could do is to influence the girl's friends. Similar situations may occur in social activities. Based on this background, we formulate a new optimization problem, the Target Influence Maximization (TIM) problem and show that this problem can be solved in polynomial-time in networks with no directed cycles. Motivated by this, we study a special strategy to construct solutions for TIM, i.e., The Target Influence Maximization through Sub graph without Directed Cycle (TIMSDC). Two polynomial-time approximation algorithms are designed for TIMSDC. Through extensive experiments on real-world data sets, we demonstrate that our algorithms work efficiently and outperform existing methods.

In many fault-detection problems, we want to identify defective items from a set of n items using the minimum number of tests. Group testing is a scenario in which each test is on a subset of items and determines whether the subset contains at least one defective item. In practice, the number d of defective items is often unknown in advance. In this paper, we present a new algorithm for the above group testing problem and prove that it has very good performance guarantee. More specifically, the number of tests used by the new algorithm is bounded from above by d log(n/d) + 3d + O(log2 d). The new algorithm is designed based on a zig-zag approach that has not been studied before and is intuitive and easy to implement. When 0 < d < ρ0n where ρ0 = 1 − 4/e2 = 0.45…, which holds for most practical applications, our new algorithm has better performance guarantee than any previous best result. Computational results show that the new algorithm has very good practical performances.

Cloud computing enables larger classes of application service providers to distribute their services to world-wide users in multiple regions without their own private data centers. Heterogeneity and resource limitation of geo-graphically distributed cloud data centers impose application service providers to have incentives to optimize their computing resource usage while guaranteeing some level of quality of service. Recent studies proposed various techniques for optimization of computing resource usage from cloud users (or application service providers) perspective with little consideration of competition. In addition, optimization efforts of application service providers motivate cloud service providers owning multiple geo-distributed clouds to decide their computing resource prices considering their efforts. In this context, we formulate this problem for cloud service providers as a game of resource pricing in geo-distributed clouds. One of the main challenges in this problem is how to model the best responses of application service providers, given resource price information of clouds in non-overlapped regions. We propose a novel concave game to describe the quantity competition among application service providers reducing payment while guaranteeing fair service delay to end users. Furthermore, we optimize the prices of computing resources to converge to the equilibrium. In addition, we show several characteristics of the equilibrium point and discuss their implications to design computing resource markets for geo-distributed clouds.

ABSTRACT In wireless communications research, a number of literature assume that every node knows all of its neighbor nodes. To this end, neighbor discovery research has been conducted, but it still has room for improvement in terms of discovery delay. Furthermore, prior work has overlooked energy efficiency, which is considered as the critical factor in wireless devices or appliances. For better performance with respect to the discovery delay and energy efficiency, we proposed a novel p‐persistent‐based neighbor discovery protocol and devised a simple and light algorithm estimating the number of neighbor nodes to support the proposed protocol. Our protocol requires a lower delay and a smaller number of messages for the discovery process than the existing protocols. For extensive performance evaluation, we adopted extra comparison targets from other research areas within the same context. Copyright © 2011 John Wiley & Sons, Ltd.

Topology control is to determine the transmission power of each node so as to maintain network connectivity and consume the minimum transmission power. Cooperative Communication (CC) is a new technology that allows multiple nodes to simultaneously transmit the same data. It can save transmission power and extend transmission coverage. However, prior research work on topology control considers CC only in the aspect of energy saving, not that of coverage extension. We observe that CC can bridge (link) disconnected networks and therefore identify the challenges in the development of a centralized topology control scheme, named shape Cooperative Bridges, which reduces transmission power of nodes as well as increases network connectivity. We propose three algorithms that select energy efficient neighbor nodes, which assist a source node to communicate with a destination node: an optimal method and two greedy heuristics. In addition, we consider a distributed version of the proposed topology control scheme. Our findings are substantiated by an extensive simulation study, through which we show that the shape Cooperative Bridges scheme substantially increases the connectivity with tolerable increase of transmission power compared to other existing topology control schemes, which means that it outperforms in terms of a connectivity-to-power ratio.

This paper investigates the fundamental performance limits of medium access control (MAC) protocols for particular multihop, RF-based wireless sensor networks and underwater sensor networks. A key aspect of this study is the modeling of a fair-access criterion that requires sensors to have an equal rate of underwater frame delivery to the base station. Tight upper bounds on network utilization and tight lower bounds on the minimum time between samples are derived for fixed linear and grid topologies. The significance of these bounds is two-fold: First, they hold for any MAC protocol under both single-channel and half-duplex radios; second, they are provably tight. For underwater sensor networks, under certain conditions, we derive a tight upper bound on network utilization and demonstrate a significant fact that the utilization in networks with propagation delay is larger than that in networks with no propagation delay. The challenge of this work about underwater sensor networks lies in the fact that the propagation delay impact on underwater sensor networks is difficult to model. Finally, we explore bounds in networks with more complex topologies.

In wireless sensor networks, virtual backbone construction based on connected dominating set is a competitive issue for routing efficiency and topology control. Assume that a sensor networks is defined as a connected unit disk graph (UDG). The problem is to find a minimum connected dominating set of given UDG with minimum routing cost for each node pair. We present a constant approximation scheme which produces a connected dominating set D, whose size |D| is within a factor α from that of the minimum connected dominating set and each node pair exists a routing path with all intermediate nodes in D and with length at most 5 · d(u,v), where d(u,v) is the length of shortest path of this node pair. A distributed algorithm is also provided with analogical performance. Extensive simulation shows that our distributed algorithm achieves significantly than the latest solution in research direction.

In this paper, we propose a new multiple-sink positioning problem in wireless sensor networks to best support real-time applications. We formally define this problem as thek-Sink Placement Problem (k-SPP) and prove that it is APX-complete. We show that an existing approximation algorithm for the well-knownk-center problem is a constant factor approximation ofk-SPP. Furthermore, we introduce a new greedy algorithm fork-SPP and prove its approximation ratio is very near to the best achievable, 2. Via simulations, we show our algorithm outperforms its competitor on average.

Topology control is one vital factor to a wireless network's efficiency. A Connected Dominating Set (CDS) can be a useful basis of a backbone topology construction. In this paper, a special CDS, named \alpha Minimum rOuting Cost CDS (\alpha-MOC-CDS), will be studied to improve the performance of CDS based broadcasting and routing. In this paper, we prove that construction of a minimum \alpha-MOC-CDS is NP-hard in a general graph and we propose a heuristic algorithm for construction of \alpha-MOC-CDS.

In this paper, we will study a special Connected Dominating Set (CDS) problem - between any two nodes in a network, there exists at least one shortest path, all of whose intermediate nodes should be included in a special CDS, named Minimum rOuting Cost CDS (MOC-CDS). Therefore, routing by MOC-CDS can guarantee that each routing path between any pair of nodes is also the shortest path in the network. Thus, energy consumption and delivery delay can be reduced greatly. CDS has been studied extensively in Unit Disk Graph (UDG) or Disk Graph (DG). However, nodes in networks may have different transmission ranges and some communications may be obstructed by obstacles. Therefore, we model network as a bidirectional general graph in this paper. We prove that constructing a minimum MOC-CDS in general graph is NPhard. We also prove that there does not exist a polynomial-time approximation algorithm for constructing a minimum MOCCDS with performance ratio plnδ, where p is an arbitrary positive number (p <; 1) and δ is the maximum node degree in network. We propose a distributed heuristic algorithm (called as FlagContest) for constructing MOC-CDS with performance ratio (1 - ln2) + 2lnδ. Through extensive simulations, we show that the results of FlagContest is within the upper bound proved in this paper. Simulations also demonstrate that the average length of routing paths through MOC-CDS reduces greatly compared to regular CDSs.

Cooperative Communication (CC) is a technology that allows multiple nodes to simultaneously transmit the same data. It can save power and extend transmission coverage. However, prior research work on topology control considers CC only in the aspect of energy saving, not that of coverage extension. We identify the challenges in the development of a centralized topology control scheme, named Cooperative Bridges, which reduces transmission power of nodes as well as increases network connectivity. We observe that CC can bridge (link) disconnected networks. We propose two algorithms that select the most energy efficient neighbor nodes, which assist a source to communicate with a destination node; an optimal method and a greedy heuristic. In addition we consider a distributed version of the proposed topology control scheme. Our findings are substantiated by an extensive simulation study, through which we show that the Cooperative Bridges scheme substantially increases the connectivity while consuming a similar amount of transmission power compared to other existing topology control schemes.

A Virtual Backbone (VB) of a wireless network is a subset of nodes such that only VB nodes are responsible for routing-related tasks. Since a smaller VB causes less overhead, size is the primary quality factor of VB. Frequently, Unit Disk Graphs (UDGs) are used to model 2D homogeneous wireless networks, and the problem of finding minimum VBs in the networks is abstracted as Minimum Connected Dominating Set (MCDS) problem in UDGs. In some applications, the altitude of nodes can be hugely different and UDG cannot abstract the networks accurately. Then, Unit Ball Graph (UBG) can replace UDG. In this paper, we study how to construct quality CDSs in UBGs in distributed environments. We first give an improved upper bound of the number of independent nodes in a UBG, and use this result to analyze the Performance Ratio (PR) of our new centralized algorithm C-CDS-UBG, which computes CDSs in UBGs. Next, we propose a distributed algorithm D-CDS-UBG originated from C-CDS-UBG and analyze its message and time complexities. Our theoretical analysis shows that the PR of D-CDS-UBG is 14.937, which is better than current best, 22. Our simulations also show that D-CDS-UBG outperforms the competitor, on average.

This paper investigates fundamental performance limits of medium access control (MAC) protocols for particular underwater multi-hop sensor networks under a fair-access criterion requiring that sensors have an equal rate of underwater frame delivery to a base station. Tight upper bounds on network utilization and tight lower bounds on minimum time between samples are derived for fixed linear topology. The paper also examines the implication of the end-to-end performance bounds regarding the traffic rate and sensing time interval of individual sensors.

It is usually possible to associate with more than one Access Point (AP) in IEEE 802.11 Wireless LANs. AP selection is a crucial issue because the performance achieved by a user heavily depends on the AP selected. A received signal strength (RSS)-based association mechanism is specified by the IEEE 802.11 standard. However, this does not consider the channel conditions and AP load, which leads to a low throughput and a low user transmission rate. An alternative to using the RSS is to exploit the airtime metric, which provides users with information on how busy the channel is, but the results of our simulations show that the airtime metric cannot indicate the exact status of the channel. In this paper, we present a new association framework using channel occupancy in order to provide users with exact channel status information of APs. Via the proposed scheme, users can compare the achievable throughput provided by each AP and select the best AP. We validate our proposed association method via simulation results, which show that the throughput improvement of the method is worthy of notice.

Connected Dominating Sets (CDSs) can serve as virtual backbones for wireless networks. A smaller virtual backbone incurs less maintenance overhead. Unfortunately, computing a minimum size CDS is NP-hard, and thus most researchers in this area concentrate on how to construct smaller CDSs. However, people neglected other important metrics of network, such as diameter and average hop distances between two communication parties. In this paper, we investigate the problem of constructing quality CDS in terms of size, diameter, and Average Backbone Path Length (ABPL). We present two centralized algorithms having constant performance ratios for its size and diameter of the constructed CDS. Especially, the size of CDS computed by the second algorithm is no more than 6.906 times of its optimal solution. Furthermore, we give its distributed version, which not only can be implemented in real situation easily but also considers energy to extend network lifetime. In our simulation, we show that in average the distributed algorithm not only generates a CDS with smaller diameter and ABPL than related work but also suppresses its size well. We also show that it is more energy efficient than others in prolonging network lifetime.

Virtual backbone has been proposed as the routing infrastructure to alleviate the broadcasting storm problem in ad hoc networks. Since the nodes in the virtual backbone need to carry other node's traffic, and node and link failure are inherent in wireless networks, it is desirable that the virtual backbone is fault tolerant. In this paper, we propose a new algorithm called Connecting Dominating Set Augmentation (CDSA) to construct a 2-connected virtual backbone which can resist the failure of one wireless node. We show that CDSA has guaranteed quality by proving that the size of the CDSA constructed 2-connected backbone is within a constant factor of the optimal 2-connected virtual backbone size. Through extensive simulations, we demonstrate that in practice, CDSA can build a 2-connected virtual backbone with only small overhead.

How to adjust the transmission power at each node to achieve global energy efficiency while maintaining the network connectivity, referred as power management problem, is the major target of various topology control technologies. Moreover, fault tolerance which is often modeled as 2-edge or 2-vertex connectivity is another desired feature in many applications. In this paper, we study the fault tolerant dual power assignment problem. With the assumption of dual universal transmission power levels, we aim to minimize the total number of nodes assigned to high power level such that the resultant network topology is 2-edge or 2-vertex connected. As the problems are NP-hard, we design a novel algorithm to compute nearly-optimal solutions. From the theoretical perspective, we prove that our algorithm can guarantee 3.67-approximation for both 2-edge connectivity and 2-vertex connectivity, which improves the existing best approximation algorithm. We also conduct some numerical experiments which show that results of our algorithm are at most 2 times of optimal solutions in average and have significant improvements compared to that of existing algorithm.

Since there is no fixed infrastructure in wireless ad hoc networks , virtual backbone has been proposed as the routing infrastructure to alleviate the broadcasting storm problem. The virtual backbone construction has been studied extensively in undirected graphs, especially in unit disk graphs, in which each node has the same transmission range. In practice, however, transmission ranges of all nodes are not necessarily equal. In this paper, we model such a network as a disk graph, where unidirectional links are considered. To study the virtual backbone construction in disk graphs, we consider two problems: strongly connected dominating set (SCDS) and strongly connected dominating and absorbing set (SCDAS). We propose a constant approximation algorithm and discuss its improvements for the SCDS problem . We also propose a heuristic for the SCDAS problem. Through extensive simulations, we verify our theoretical analysis and also demonstrate that the SCDS can be extended to form an SCDAS with marginal extra overhead.

This paper introduces the problem of fault tolerant topology control for all-to-one and one-to-all communication in static wireless networks with asymmetric wireless links. This problem is important in both theoretical and practical aspects. We investigate two approaches, namely minimum weight based approach and nearest neighbor augmentation approach, to address this problem. Furthermore, we give theoretical analysis for the proposed algorithms. Among other results, we show that the minimum weight based approach has a $k$-approximation algorithm for all-to-one fault tolerant topology control where $k$ is the number of disjoint paths. When $k=1$, this approach solves the minimum power all-to-one $1$-connected topology control problem. To the best of our knowledge, this paper is the first to study the fault tolerant topology control for all-to-one and one-to-all communication in asymmetric static wireless networks, and also is the first to demonstrate that the minimum power all-to-one 1-connected topology control problem has an optimal solution.

Since there is no fixed infrastructure or centralized management in wireless ad hoc networks, a Connected Dominating Set (CDS) has been proposed to serve as a virtual backbone. The CDS of a graph representing a network has a significant impact on the efficient design of routing protocols in wireless networks. This problem has been studied extensively in Unit Disk Graphs (UDG), in which all nodes have the same transmission ranges. However, in practice, the transmission ranges of all nodes are not necessarily equal. In this paper, we model a network as a disk graph and introduce the CDS problem in disk graphs. We present two efficient approximation algorithms to obtain a minimum CDS. The performance ratio of these algorithms is constant if the ratio of the maximum transmission range over the minimum transmission range in the network is bounded. These algorithms can be implemented as distributed algorithms. Furthermore, we show a size relationship between a maximal independent set and a CDS as well as a bound of the maximum number of independent neighbors of a node in disk graphs. The theoretical analysis and simulation results are also presented to verify our approaches.

Energy conservation is an important concern in wireless networks. Many algorithms for constructing a broadcast tree with minimum energy consumption and other goals have been developed. However, no previous research work considers the total energy consumption and transmission delays of the broadcast tree simultaneously. In this paper, based on an (alpha, beta)-tree, a novel concept to wireless networks, we define a new strongly connected broadcast arborescence with bounded transmission delay (SBAT) problem and design the strongly connected broadcast arborescence (SBA) algorithm with linear running time to construct a strongly connected broadcast tree with bounded total power, while satisfying the constraint that the transmission delays between the source and the other hosts are also bounded. We also propose the distributed version of the SBA algorithm. The theoretical analysis and simulation results show that the SBA algorithm gives a proper solution to the SBAT problem

This paper presents various new techniques on secure group communication schemes. We present a new broadcast encryption scheme RBE, being particularly efficient in multiple revocation, and a node-based key pre-distribution scheme, remedying the key overlapping problem of pool-based schemes. Starting with a detailed analysis on broadcast encryption and group key distribution schemes, we discuss the influence of join as well as the feasibility of including it in broadcast encryption schemes by means of performing full updating or overprovisioning.

Due to the limited power supplies of a wireless node, energy efficiency is a crucial aspect to the design of a broadcast protocol. In the minimum energy broadcast problem, each node adjusts its transmission power to minimize the total energy consumption. The minimum energy broadcast problem is proved to be NP-Complete. The Hitch-hiking model introduced recently in [M. Agarwal et al., (2004)] takes advantage of the physical layer to combine partial signals containing the same data in order to decode a complete message. Moreover, the wireless multicast advantage (WMA), that is a single transmission can be received by all the nodes that are within the transmission range of a transmitting node, reduces the total energy of the broadcast tree. In this paper, we take advantages of both Hitch-hiking and WMA to design an energy-efficient broadcast tree algorithm with Hitch-hiking (BHH). The simulation results show that BHH reduces the total energy of the broadcast tree greatly.

In mobile ad-hoc networks, hosts communicate with each other without the help of any physical infrastructure. Inevitably, the communication tends to be less efficient in terms of computational and communicational overhead. Recent studies have shown that virtual backbone can help reduce the communication overhead. However, the backbone structure is very vulnerable due to several reasons, e.g., node mobility and unstable links, etc. In this paper, we introduce a localized virtual backbone construction scheme, connected maximal independent set with multiple initiators (MCMIS), which takes node stability into consideration and can construct the backbone quickly. We design MCMIS aiming at three goals: small backbone size, fast construction, stable backbone. Through extensive simulations, we find that our scheme could obtain a better performance on stability and backbone size than other localized schemes.

Position-based reactive routing is a scalable solution for routing in mobile ad hoc networks. The route discovery algorithm in position-based routing can be efficiently implemented only if the source knows the current address of the destination. In this paper, a quorum-based location management scheme is proposed. Location servers are selected using the minimum dominating set (MDS) approach, and are further organized into quorums for location update and location query. When a mobile node moves, it updates its location servers in the update quorum; when a node requests the location information of another node, it will send a query message to the location servers in the query quorum. We propose to use the position-based quorum system, which is easy to construct and guarantees that the update quorums always intersect with the query quorums so that at least one location server in the query quorum is aware of the most recent location of the mobile node. Clusters are introduced for large scale ad hoc networks for scalability. Experiment results show that the proposed scheme provides good scalability when network size increases. Copyright © 2005 John Wiley & Sons, Ltd.

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.

This work discusses the energy efficient QoS topology control problem in ad hoc wireless networks. Given a set of nodes in a plane, end-to-end traffic demands and delay bounds between node pairs, the problem is to find a network topology that can meet the QoS requirements and the maximum transmitting power of nodes is minimized. We consider two cases of the problem: 1) the traffic demands are not splittable, and 2) the traffic demands are splittable. For the former case, the problem is formulated as an integer linear programming problem. For the latter case, the problem is formulated as a mixed integer programming problem, and an optimal algorithm has been proposed to solve the problem.

In wireless ad-hoc networks, hosts communicate with each other without help of any physical infrastructure. Inevitably, the communication tends to be inefficient in terms of computational and network resources. Study on virtual infrastructures or backbones in wireless ad-hoc networks gets more attention in the hope of reducing the communication overhead. But the backbone structure is very vulnerable due to various factors like node mobility, unstable links, and so on. So a new scheme which is reliable and efficient both to construct and maintain the backbone structure is needed. We present our noble virtual backbone scheme which is reliable and efficient by considering stability and coverage of nodes.

In ad hoc wireless networks, to compute the transmission power of each wireless node such that the resulting network is connected and the total energy consumption is minimized is defined as a Minimum Energy Network Connectivity (MENC) problem, which is an NP-complete problem. In this paper, we consider the approximated solutions for the MENC problem in ad hoc wireless networks. We present a theorem that reveals the relation between the energy consumption of an optimal solution and that of a spanning tree and propose an optimization algorithm that can improve the result of any spanning tree-based topology. Two polynomial time approximation heuristics are provided in the paper that can be used to compute the power assignment of wireless nodes in both static and low mobility ad hoc wireless networks. The two heuristics are implemented and the numerical results verify the theoretical analysis.

This paper considers the problem of broadcasting in large ad hoc wireless networks. We focus on the energy-efficient broadcast routing in stationary networks and consider the case where wireless nodes can dynamically control their transmission power for each broadcast session. The minimum spanning tree (MST) has the property that the longest edge in the tree is the shortest among all the spanning trees, We introduce a new algorithm called minimum longest edge (MLE) that constructs a broadcast tree using MST. This algorithm provides a scheme to balance the energy consumption among all nodes. The simulation results show that MLE improves the energy balance and network lifetime for a wide range of networks, and the improvement is more significant when the network size increases.

This paper investigates the optimal placement of proxies of a Web server on the Internet, with the consideration of both read and update operations to the data on the Web server. We first study the problem of optimal placement of $k$ proxies in a system to minimize the total access cost to the Web server. Then, for an unknown number of proxies, we find the optimal number of proxies required in the system. The problems are formulated by using the dynamic programming method and the optimal solutions are obtained. Simulations have been conducted to evaluate the performance of the proposed algorithms and to demonstrate how the effectiveness of proxy placement is affected by various factors, such as network traffic load, number of proxies, read–write ratio and proxy hit ratio.

Abstract A connected dominating set in a graph is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected. A minimum‐connected dominating set is such a vertex subset with minimum cardinality. An application in ad hoc wireless networks requires the study of the minimum‐connected dominating set in unit‐disk graphs. In this paper, we design a (1 + 1/s)‐approximation for the minimum‐connected dominating set in unit‐disk graphs, running in timenO((slogs)2). © 2003 Wiley Periodicals, Inc.

An important goal of the design of WDM (wavelength division multiplexing) networks is to use less wavelengths to serve more communication needs. According to the wavelength conflict rule, we know that the number of wavelengths required in a WDM network is at least equal to the maximal number of channels over a fiber (called maximal link load) in the network. By placing wavelength converters at some nodes in the network, the number of wavelengths needed can be made equal to the maximal link load. In this paper we study the problem of placing the minimal number of converters in a network to achieve that the number of wavelengths in use is equal to the maximal link load. For duplex communication channels, we prove that an optimal solution can be obtained in polynomial-time. For unidirectional communication channels, which was proved to be NP-complete, we develop a set of lemmas which lead to an efficient approximation algorithm whose approximation ratio is two.

A cyclic consecutive-k-out-of-n: G system consists of n components lying on a cycle. Those components are exchangeable but may have different working probabilities. The system works if and only if there are k consecutive components at work. What is the optimal assignment of components for maximizing the reliability of the system? Does the optimal assignment depend on the working probability values of components? For $k \leq n \leq 2k+1$, Zuo and Kuo in 1990 proposed a solutionindependent from the working probability values of components, called the invariant optimal assignment. However, their proof is incomplete, pointed out recently by Jalali et al. [The Optimal Consecutive-k-out-of-n: G Line for $n \leq 2k$}, manuscript, 1999]. We present a complete proof in this paper.

This paper investigates the optimal placement of proxies of a Web server on the Internet. With the consideration of both read and write operations to the data on the Web server. First, we study the problem of optimal placement of k proxies in a system to minimize the total access cost to the Web server. Then, for unknown number of proxies, we find the optimal number of proxies required in the system. The problems are formulated using a dynamic programming method and optimal solutions are obtained. Intensive simulations have been conducted to evaluate the performance of the proposed algorithms, and to demonstrate the relationship between the number of proxies required in the system and the read-write ratio. This work can significantly alleviate the Web access traffic on the Internet and improve the performance of the Web server.

This paper investigates the issues of the optimal placement of a limited number of Web proxies in an environment where a Web site is replicated (i.e. mirrored Web sites). Two different objectives are studied: minimizing the overall access cost by all clients to the Web site and minimizing the longest delay for any client to access the Web site. The problem is reduced to the placement of proxies in a set of trees whose root nodes are the server replicas. It is then formulated and solved by using a dynamic programming method. The significance of this work includes: (1) alleviating the Internet traffic of Web accesses; (2) improving the response time of Web page accesses; (3) maximizing Web server performance by using a limited number of proxies.

Given a WDM optical network with wavelength channels on its fiber links, we consider the problem of finding the minimum set of network nodes such that, with wavelength converters at these nodes, broadcast can be supported in the network. We call this problem the converter placement problem. We model a given network using a graph G with colors on its edges and give a mathematical formulation for the problem based on the graph model. Two related problems, color-covering and vertex color-covering, are given and analyzed. Both of them are shown to have a polynomial-time approximation with performance ratio ln n+1 and ln n is the best possible performance ratio unless NP /spl sub/ DTIME(n/sup poly log n/), where n is the number of vertices in G. Using these results, we show that the Converter Placement problem has a polynomial-time approximation with performance ratio 2(ln n+1) and 1/2 ln n is the best possible performance ratio unless NP /spl sub/ DTIME(n/sup poly log n/). We present an approximation algorithm to solve the converter placement problem and study the performance of the algorithm on randomly generated network topologies.

This paper discusses quality-of-service (QoS) multicast in wavelength-division multiplexing (WDM) networks. Given a set of QoS multicast requests, we are to find a set of cost suboptimal QoS routing trees and assign wavelengths to them. The objective is to minimize the number of wavelengths in the system. This is a challenging issue. It involves not only optimal QoS multicast routing, but also optimal wavelength assignment. Existing methods consider channel setup in WDM networks in two separate steps: routing and wavelength assignment, which has limited power in minimizing the number of wavelengths. In this paper, we propose a new optimization method, which integrates routing and wavelength assignment in optimization of wavelengths. Two optimization algorithms are also proposed in minimizing the number of wavelengths. One algorithm minimizes the number of wavelengths through reducing the maximal link load in the system; while the other does it by trying to free out the least used wavelengths. Simulation results demonstrate that the proposed algorithms can produce suboptimal QoS routing trees and substantially save the number of wavelengths.

In multihop systems of wavelength division multiplexing (WDM) networks, wavelength conversion is required at the conjunction of two lightpaths if they use different wavelengths. We consider the problem of assigning wavelengths to the lightpaths by using a limited number of wavelengths, so that the overall number of wavelength conversions in the whole system is minimal. The problem is formulated as a maximum clique cover problem. An approximation algorithm is proposed to solve it. Our proposed theory also illustrates the tradeoff relationship between the number of wavelengths and the number of conversions in the system.

Finding the longest path and the worst delay is the most important task in static timing analysis. But in almost every digital circuit, there exists false paths which are logically impossible or designers don't care about their delays. This paper presents a new method to calculate the worst delay of a circuit with known false paths. When searching for the longest path, it stores delays on nodes conditionally with false paths matched up to the node, thus reduces the number of cache entries and eliminates revisits. This method can be applied to incremental delay calculation with little change. Experiments show that the new method is significantly better than path enumeration without conditional cache.

Investigates the issues of placing a limited number of Web proxies in an environment where the Web server is replicated (i.e. mirrored Web servers). Two different objectives are considered: (a) minimizing the overall access cost by all clients of the Web server, and (b) minimizing the longest delay for any client to access the Web server. The problems are formulated and solved by using a dynamic programming method. This work can: (1) alleviate the amount of Internet traffic incurred by fast-growing Web accesses; (2) improve the response time of Web server accesses; and (3) maximize Web server performance by using a limited number of proxies.

This paper studies three-stage Clos (1953) switching networks for multicast communications in terms of their blocking probabilities on a random traffic model. Even though the lack of multicast capability in input-stage switches requires a prohibitively large number of middle switches to provide compatible requests with nonblocking paths, the probabilistic model gives an observation that the blocking probability decreases drastically and then approaches zero as the number of middle switches is far less than the theoretical bound. The S-shaped curves of blocking probability versus degree of fanout indicate that high fanout requests are mostly blocked at some given reference network utilization. A split routing algorithm and its blocking probability are introduced to enhance the routability of the high fanout requests. We also corroborate the analytic model by performing network simulations based on a random request generator and a random routing strategy.

Chung and Ross [SIAM J. Comput., 20 (1991), pp. 726--736] conjectured that the multirate three-stage Clos network C(n,2n-1,r) is rearrangeable in the general discrete bandwidth case; i.e., each connection has a weight chosen from a given finite set {p 1 , p 2 ,. . .,p k } where $1 \geq p_1 > p_2 > \cdots > p_k > 0$ and p i is an integer multiple of p i , denoted by $p_k \mid p_i$, for $1 \leq i \leq k-1$. In this paper, we prove that multirate three-stage Clos network C(n,2n-1,r) is rearrangeable when each connection has a weight chosen from a given finite set {p 1 , p 2 ,. . .,p k } where $1 \geq p_1 > p_2 > \cdots > p_{h} > 1/2 \geq p_{h+1} > \cdots > p_k > 0$ and p h+2 | p h+1 ,p h+3 |p h+2 ,. . . ,p k | p h+1 . We also prove that C(n,2n-1,r) is two-rate rearrangeable and $C(n, \lceil \frac{7n}{3} \rceil, r)$ is three-rate rearrangeable.

We present the problem of constructing roads of minimum total length to interconnect n highways under the constraint that the roads can intersect each highway only at one point in a designated interval which is a line segment. We present a set of optimality conditions for the problem and show how to construct a solution to meet this set of optimality conditions.

In this paper, we study the pyramid network (also called pyramid), one of the important architectures in parallel computing, network computing, and image processing. Some properties of pyramid networks are investigated. We determine the line connectivity and the fault diameters in pyramid networks. We show how to construct a path between two nodes in the faulty pyramid networks in polynomial time. A polynomial-time algorithm is also given for generating the containers in pyramid networks. Our results show that pyramid networks have very good fault tolerance properties.

In the multirate switching environment each (connection) request is associated with a bandwidth weight. We consider a three-stage Clos network and assume that each link has a capacity of one (after normalization). The network is rearrangeable if for all possible sets of requests such that each input and output link generates a total weight not exceeding one, there always exists a set of paths, one for each request, such that the sum of weights of all paths going through a link does not exceed the link capacity. The question is to determine the minimum number of center switches which guarantees rearrangeability. We obtain a lower bound of 11n/9 and an upper bound of 41n/16. We then extend the result for the three-stage Clos network to the multistage Clos network. Finally, we propose the weighted version of the edge-coloring problem, which somehow has escaped the literature, associated with our switching network problem.

A Steiner minimum tree (SMT) is the shortest-length tree in a metric space interconnecting a set of points, called the regular points, possibly using additional vertices. A k-size Steiner minimum tree (kSMT) is one that can be split into components where all regular points are leaves and all components have at most k leaves. The k-Steiner ratio, $\rho_{k}$, is the infimum of the ratios SMT/kSMT over all finite sets of regular points in all possible metric spaces, where the distances are given by a complete graph. Previously, only $\rho_{2}$ and $\rho_{3}$ were known exactly in graphs, and some bounds were known for other values of k. In this paper, we determine $\rho_{k}$ exactly for all k. From this we prove a better approximation ratio for the Steiner tree problem in graphs.

The satisfiability (SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design efficient algorithms to find a solution for a satisfiable conjunctive normal form (CNF) formula. A new formulation, the universal SAT problem model, which transforms the SAT problem on Boolean space into an optimization problem on real space has been developed (J. Gu, 1988; 1992; 1994). Many optimization techniques, such as the steepest descent method, Newton's method, and the coordinate descent method, can be used to solve the universal SAT problem. We prove that when the initial solution is sufficiently close to the optimal solution, the steepest descent method has a linear convergence ratio /spl beta/<1, Newton's method has a convergence ratio of order two, and the convergence ratio of the steepest descent method is approximately (1-/spl beta//m) for the universal SAT problem with m variables. An algorithm based on the coordinate descent method for the universal SAT problem is also presented. Experimental results show that this algorithm is more efficient than some previous ones in finding a solution for certain classes of the satisfiable CNF formulas.

Article The k-Steiner ratio in graphs Share on Authors: Al Borchers Department of Computer Science, University of Minnesota, Minneapolis, MN Department of Computer Science, University of Minnesota, Minneapolis, MNView Profile , Ding-Zhu Du Department of Computer Science, University of Minnesota, Minneapolis, MN Department of Computer Science, University of Minnesota, Minneapolis, MNView Profile Authors Info & Claims STOC '95: Proceedings of the twenty-seventh annual ACM symposium on Theory of computingMay 1995 Pages 641–649https://doi.org/10.1145/225058.225282Online:29 May 1995Publication History 8citation586DownloadsMetricsTotal Citations8Total Downloads586Last 12 Months13Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimum possible total length. The Steiner ratio for a metric space is the largest lower bound for the ratio of lengths between a minimum Steiner tree and a minimum spanning tree on the same set of points in the metric space. In this note, we show that for any Minkowski plane, the Steiner ratio is at least 2/3. This settles a conjecture of D. Cieslik, and also Du et al.

The uniqueness of continuous multimedia database applications lies in the fact that they require system support steady flow of media access data. In this paper we address the problem of system resource management for such applications. We introduce a session-based scheduling paradigm that, unlike traditional task scheduling, enables scheduling of all processing entities (threads, I/O processes, and buffers) across multiple system resources for guarantee of steady mediaflow. Under this paradigm, we develop an approach to on-line generation of session resource requirements based on resource allocation tradeoffs. Further, we develop a multidimensional "bin-packing" approach to allocation and scheduling of multiple resources for concurrent sessions. The goal is to minimize resource overheads and maximize the number of concurrent sessions while meeting session timing constraints and resource capacity constraints.>

Abstract We propose a new routing strategy for the KYKLOS II multiprocessor interconnection network that achieves minimum distance for the path between any two processors. For KYKLOS II with 2n processors, the average distance is shorter than those of previous routing strategies by approximately 2 log2n. The traffic density, a measure of traffic concentration, is better than previous strategies for up to 2000 processors, though asymptotically inferior to a strategy proposed by Jenevein and Menezes. © 1994 by John Wiley & Sons, Inc.

In many fault detection problems, the goal is to identify defective items from a set of items with a minimum number of tests. Each test is on a subset of items, which tells whether the subset contains a defective item or not. The concept of competitive algorithm has been developed to relate the properties of the group testing algorithms that assume that the number of defective items d is known, to those without any a priori knowledge on d. A new concept of strongly competitive algorithm is defined that relates different characteristics of these two classes of algorithms and present an interesting relationship between the two concepts competitive and strongly competitive. A strongly competitive algorithm is also presented.

Many fault-detection problems fall into the following model: There is a set of n items, some of which are defective. The goal is to identify the defective items by using the minimum number of tests. Each test is on a subset of items and tells whether the subset contains a defective item or not. Let $M_\alpha (d,n)(M_\alpha (d|n))$ denote the maximum number of tests for an algorithm $\alpha $ to identify d defectives from a set of n items provided that d, the number of defective items, is known (unknown) before the testing. Let $M(d,n) = \min _\alpha M_\alpha (d,n)$. An algorithm a is called a competitive algorithm if there exist constants c and a such that for all $n > d > 0,M_\alpha (d|n) \leqslant cM(d,n) + a$. This paper confirms a recent conjecture that there exists a bisecting algorithm A such that $M_A (d|n) \leqslant 2M(d,n) + 1$. Also, an algorithm B such that $M_B (d|n) \leqslant 1.65M(d,n) + 10$ is presented.

A graph has spread (m, k, l) if for any m+1 distinct nodes x, y/sub 1/, . . ., y/sub m/ and m positive integers r/sub 1/, . . ., r/sub m/, such that Sigma /sub i/r/sub i/=k, there exist k node-disjoint paths of length at most 1 from x to the y/sub i/, where r/sub i/ of them end at y/sub i/. This concept contains, and is related to many important concepts used in communications and graph theory. The authors prove an optimal general theorem about the spreads of digraphs generated by line digraph iterations. Useful graphs, like the de Bruijn and Kautz digraphs, can be thus generated. The theorem is applied to the de Bruijn and Kautz digraphs to derive optimal bounds on their spreads, which implies previous results and resolves open questions on their connectivity, diameter, k-diameter, vulnerability, and some other measures related to length-bound disjoint paths.>

In this paper we present a new binary-programming formulation for the Steiner problem in graphs (SPG), which is well known to be NP-hard. We use this formulation to generate test problems with known optimal solutions. The technique uses the KKT optimality conditions on the corresponding quadratically constrained optimization problem.

Consider a set P of points in a normed space whose unit sphere is a d-dimensional symmetric polytope with 2d extreme points. This paper proves that there always exists a Steiner minimum tree whose Steiner points are located only at points whose coordinates appear in points of P. This generalizes a recent result of Snyder on d-dimensional rectilinear space, which itself extends Hanan’s well-known and much quoted result on the rectilinear plane. Furthermore, the proof in this paper is much simpler than Snyder’s proof, even considerably shorter than Hanan’s proof. A consequence of this result is that the Steiner problem for P in such a space is reduced to a Steiner problem on graphs and is solvable by any existing Steiner graph algorithms. The paper also conjectures that such a reduction is impossible if the polytope has more than $2d$ extreme points and provides partial support for the conjecture.

Finding a shortest network interconnecting a given set of points in the Euclidean plane (a Steiner minimum tree) is known to be NP-hard. It is shown that there exists a polynomial-time heuristic with a performance ratio bigger than square root 3/2.>

A family of finitely many continuous functions on a polytope X, namely (g/sub i/(x))/sub i in I/, is considered, and the problem of minimizing the function f(x)=max/sub i in I/g/sub i/(x) on X is treated. It is shown that if every g/sub i/(x) is a concave function, then the minimum value of f(x) is achieved at finitely many special points in X. As an application, a long-standing problem about Steiner minimum trees and minimum spanning trees is solved. In particular, if P is a set of n points on the Euclidean plane and L/sub s/(P) and L/sub m/(P) denote the lengths of a Steiner minimum tree and a minimum spanning tree on P, respectively, it is proved that, for any P, L/sub S/(P)>or= square root 3L/sub m/(P)/2, as conjectured by E.N. Gilbert and H.O. Pollak (1968).>

Abstract The problem under consideration arises from studies on local networks and multimodule memory organizations. The ring network has been one of the popular network topologies used in the design and implementation of local area networks and other configurations. We consider here a generalization of the ring network by adding two fixed‐step links to each node. The resulting networks have low diameter, easy routing, and switching structure and therefore are suitable for implementation in the design of reliable networks. Let N denote the number of nodes in the network. For a given N, we are concerned with the problem of determining the best topologies to minimize the diameter (and, hence, the transmission delay) of the network. We obtain new classes of values of N for which topologies can be found that achieve the lower bound lb = [(√2N ‐ 1 ‐ 1)/2] for the minimum diameter. We also show that for some infinite classes of N this lower bound lb is not achievable.

Consider a system with n components and a reliability function $R(x_1 , \cdots ,x_n )$ where $x_j $ is the reliability of component j. Suppose that each component consists of the same set of parts, say $h_i $ parts of type i for $i = 1, \cdots ,m$, which must all work for the component to work. The problem is to assign $nh_i $ parts of type $i,i = 1, \cdots ,m$, with various part reliabilities to the n components to maximize the system reliability. An assignment is called monotone if all the best parts go to one component, all the next best parts go to the second component, and so on. The optimality of monotone assignments for systems with symmetric and asymmetric reliability functions is studied. In particular, it is proved that monotone assignments are optimal for s-stage k-out-of-n systems.

Abstract We show that the digraphs proposed independently by Imase and Itoh, and Reddy, Pradhan and Kuhl to minimize diameters essentially retain all the nice properties of de Bruijn digraphs and yet are applicable to any number of nodes. In particular we give results on the number of loops, the link connectivities and connectivities, the embedding properties and the self‐routing properties for these digraphs.

A problem arising in the design of vacuum systems and having applications to some natural problems of interconnection design is described as follows. (1) Given a set X and subsets $X_i ,Y_i $ of $X,i = 1, \cdots ,n$, satisfying $X_i \cap Y_i = \O $, find a graph G with vertex set X and the minimum number of edges such that for any i, the subgraph induced by $X\backslash Y_i $ has a connected component containing $X_i $. Two other problems related to this one are the following ones. (2) Given a set X and subsets $X_1 ,X_2 , \cdots ,X_n $ such that $X = \cup _{i = 1}^n X_i $, find a graph G with vertex set X and the minimum number of edges such that for any i the subgraph $G_i $ induced by $X_i $ in G is connected. (3) Given a set X and subsets $X_1 ,X_2 , \cdots ,X_n $ such that $X = \cup _{i = 1}^n X_i $, find a graph G with vertex set X, find a graph G with vertex set X and the minimum number of edges such that for any subset I of $\{ 1, \cdots ,n \}$, the subgraph induced by $ \cap _{i \in I} X_i $ is connected. This paper shows that (3) is polynomial-time solvable while (1) and (2) are NP-complete. Also, some heuristics for (1) and (2) are given. The solution of (3) is an interesting application of matroid theory.

If C is a class of sets and A is not in C , then an infinite set H is a proper hard core for A with respect to C , if H ⊆ A and for every C ε C such that C ⊆ A , C ⋒ H is finite. It is shown that if C is a countable class of sets of strings that is closed under finite union and finite variation, then every infinite set not in C has a proper hard core with respect to C . In addition, the density of such generalized complexity cores is studied.

Article Free Access Share on A note on one-way functions and polynomial-time isomorphisms Authors: K I Ko Department of Computer Science, University of Houston, Houston, Tx and Mathematical Sciences Research Institute, Berkeley, Ca. Department of Computer Science, University of Houston, Houston, Tx and Mathematical Sciences Research Institute, Berkeley, Ca.View Profile , T J Long Department of Computer and Information Science, The Ohio State University, Columbus, Oh. Department of Computer and Information Science, The Ohio State University, Columbus, Oh.View Profile , D Z Du Mathematical Sciences Research Institute, Berkeley, Ca. Mathematical Sciences Research Institute, Berkeley, Ca.View Profile Authors Info & Claims STOC '86: Proceedings of the eighteenth annual ACM symposium on Theory of computingNovember 1986 Pages 295–303https://doi.org/10.1145/12130.12160Published:01 November 1986Publication History 4citation223DownloadsMetricsTotal Citations4Total Downloads223Last 12 Months12Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Abstract Recently Trietsch and Handler extended a conjecture of Pollak and Gilbert on the Steiner ratio to a model first studied by Gilbert where the cost of an edge is flow dependent. For three given points Trietsch and Handler showed that the maximum Steiner ratio is achieved when the cost is independent of the flow, i. e., the extended conjecture is reduced to the original conjecture. They also conjectured that the two conjectures are equivalent for any number of given points. In this paper we give a counterexample to their conjecture if the number of given points is at least four. We also replace their proof for the three‐point case, which depends heavily on computer‐aided calculations, by a simple geometric proof.

Abstract A consecutive‐2 system is a graph where each vertex can either work or fail and the system fails if and only if two vertices incident to the same edge both fail. The simplest probability structure attached to such systems is to assume that vertex i has probability p i of failing and the states of the vertices are stochastically independent. For a given graph G of n vertices and a given set P of n probabilities, an optimal consecutive‐2 system is the triple ( G,P,M ), where M is a mapping from P to the vertices of G such that the probability of the system failing is minimum. Consecutive‐2 systems have been widely studied when the graph is either a line or a cycle. In this paper we study optimal consecutive‐2 systems which consist of many lines or many cycles. Our results provide optimal mappings that depend only on the rankings of the individual failure probabilities and not on their actual values. Moreover, we show by examples that rankings alone are probably insufficient to solve cases more complex than those solved in this paper.

We consider networks of processors where each processor either has one in-link and one out-link, or two in-links and two out-links. We study three properties of such networks: 1) diameter, 2) connectivity, and 3) the ring property. We propose a class of networks which seem to achieve the optimum as far as these three properties are concerned.