This paper presents FLEX, a real-time scheduling framework that adaptively allocates limited machine attention (i.e., computing resources) among different spatial views (partitioned by camera facing directions) and sensory modalities (i.e., LiDAR and cameras) within multi-modal multi-view machine perception on resource-constrained embedded platforms. It is achieved through the effective wiring of two features: First, considering the heterogeneous and time-varying criticality among views and modalities within dynamic sensing contexts (i.e., object locations), we calibrate an “anytime” multi-modal perception pipeline that dynamically adjusts the modality fusion strategies of each view. Second, to optimize the GPU processing throughput with time guarantees, FLEX centers around an adaptive batch scheduling algorithm that intelligently groups consecutive asynchronous view inspection tasks based on the job sequence1generated from a non-preemptive EDF schedule to maximize a measure of system utility, with the runtime elastic fusion used as a subroutine. Temporal load balancing is maintained during the scheduling by always ensuring the sequential schedulability of future tasks in early batching decisions. We implement FLEX on NVIDIA Jetson Orin and conduct extensive experiments with a large-scale driving dataset. The results demonstrate the superiority of FLEX in improving perception quality and system throughput with time guarantees.1Following the real-time conventions, we use “job” to denote the instance of periodic tasks.

We consider the minimum delay routing problem in stochastic queueing networks where the goal is to find the optimal static routing policy that minimizes the average delay in the network. Previous works on minimum delay routing rely on knowledge of the delay function that maps the routing policies to their corresponding average delay, which is typically unavailable in stochastic queueing networks due to the complex dependency of the delay function on the distributional characteristics of network links. In this paper, we propose a learning approach to the minimum delay routing problem, whereby instead of relying on aprior information on the delay function, we seek to learn the delay function through observations. We design an algorithm that leverages finite-time observations of network queue lengths to approximate the values of the delay function, uses the approximate values to estimate the gradient of the delay function, and performs gradient descent based on the estimated gradient to optimize the routing policy. We prove that our algorithm converges to the optimal static routing policy when the delay function is convex, which is a reasonable condition in practical settings. We conduct extensive simulations to evaluate the empirical performance of our algorithm, demonstrating its superior delay performance over static policies and even dynamic policies such as Join-the-Shortest-Queue and BackPressure.

We consider the optimal routing problem in a discrete-time system with a job dispatcher connected to$M$parallel servers. At every time slot, the job dispatcher sends the incoming jobs to a server for execution, with each server having a queue that stores the jobs. The arrival process of incoming jobs, and the service processes of the servers are stochastic with unknown and possibly heterogeneous rates. Each server$s_{m}$is associated with an underlying utility$v_{m}$that is initially unknown. Whenever server$s_{m}$completes a job, a utility of$v_{m}$is obtained and a noisy observation of$v_{m}$is received. The goal is to design a policy that makes routing decisions to maximize the total utility obtained by the end of a finite time horizon$T$. The performance of policies is measured in terms of regret, which is the additive difference between the expected total utility obtained by the policy and the supremum of the expected total utility over all the policies. The optimal routing problem can be interpreted as a problem of multi-armed bandit with queues where each server is viewed as an arm and the completion of a job is viewed as a pull of an arm. The key distinction between the optimal routing problem and traditional multi-armed bandit problems is in the queueing dynamics at the server, which arises due to the stochastic nature of the arrival and service processes. Our results combine techniques from control of stochastic queueing systems and stochastic multi-armed bandits to provide insights to the design and analysis of policies for the optimal routing problem. We first present analytical bounds that link the regret to the utilization and queue length of servers. Next, we start by assuming that the ordering of the underlying utilities is known and introduce the Priority-$K$routing policy which makes priority-based routing decisions that send the incoming jobs to the server of the highest underlying utility with queue length no larger than a threshold$K$. We prove that Priority-$K$achieves$O(\log T)$-regret with an appropriately chosen$K$. Next, removing the assumption of known utility ordering, we propose the Upper-Confidence Priority-$K$policy, which essentially combines the Priority-$K$policy with the ordering based on the upper-confidence bounds of the underlying utilities, and establish that the Upper-Confidence Priority-$K$policy achieves an instance-dependent$O(\log ^{3} T)$-regret. Finally, we extend our results to the a generalized version of the optimal routing problem with multiple job dispatchers in a bipartite network. Our theoretical results are also validated by simulations.

This paper presents a real-time multi-view scheduling framework for DNN-based live video analytics at the edge to minimize frame processing latency. The work is motivated by applications where a higher frame rate is important, not to miss actions of interest. Examples include defense, border security, and intruder detection applications where sensors (in this paper, cameras) are deployed to monitor key roads, chokepoints, or passageways to identify events of interest (and intervene in real-time). Supporting a higher frame rate entails lowering frame processing latency. We assume that multiple cameras are deployed with partially overlapping views. Each camera has access to limited onboard computing capacity. Many targets cross the field of view of these cameras (but the great majority do not require action). We take advantage of the spatial-temporal correlations among multi-camera video streams to perform target-to-camera assignment such that the maximum frame processing time across cameras is minimized. Specifically, we use a data-driven approach to identify objects seen by multiple cameras, and propose a batch-aware latency-balanced (BALB) scheduling algorithm to drive the object-to-camera assignment. We empirically evaluate the proposed system with a real-world surveillance dataset on a testbed consisting of multiple NVIDIA Jetson boards. The results show that our system substantially improves the video processing speed, attaining multiplicative speedups of 2.45× to 6.85×, and consistently outperforms the competitive static region partitioning strategy.

Consider a stream learning system with a source and a set of computation nodes that solves a machine learning task modeled as stochastic convex optimization problem over an unknown distribution D. The source generates i.i.d. data points from D and routes the data points to the computation nodes for processing. The data points are processed in a streaming fashion, i.e., each data point can be accessed only once and is discarded after processing. The system employs local stochastic gradient descent (local SGD), where each computation node performs stochastic gradient descent locally using the data it receives from the source and periodically synchronizes with other computation nodes. Since the routing policy of the source determines the availability of data points at each computation node, the performance of the system, i.e., the optimization error obtained by local SGD, depends on the routing policy.In this paper, we study the influence of the routing policy on the performance of stream learning systems. We first derive an upper bound on the optimization error as a function of the routing policy. The upper bound reveals that the routing policy influences the performance through tuning the bias-variance trade-off of the optimization process, and gives rise to a framework for optimizing the routing policy for stream learning systems. By minimizing the upper bound, we propose an optimal static routing policy that achieves the best trade-off for stream learning systems with deterministic data generation process. We then propose a routing policy that can approximate the optimal static routing policy arbitrarily closely for systems where the data points are generated according to a stochastic process with unknown rate. Finally, we conduct simulations using Support Vector Machine as the machine learning task on a real data set, and show that the optimal static routing policy has excellent empirical performance in terms of minimizing the optimization error and the proposed stochastic routing policy closely matches the optimal static routing policy.

This paper presents a self-cueing real-time frame-work for attention prioritization in AI-enabled visual perception systems that minimizes a notion of state uncertainty. By attention prioritization we refer to inspecting some parts of the scene before others in a criticality-aware fashion. By self-cueing, we refer to not needing external cueing sensors for prioritizing attention, thereby simplifying design. We show that attention prioritization saves resources, thus enabling more efficient and responsive real-time object tracking on resource-limited embedded platforms. The system consists of two components: First, an optical flow-based module decides on the regions to be viewed on a subframe level, as well as their criticality. Second, a novel batched proportional balancing (BPB) scheduling policy decides how to schedule these regions for inspection by a deep neural network (DNN), and how to parallelize execution on the GPU. We implement the system on an NVIDIA Jetson Xavier platform, and empirically demonstrate the superiority of the proposed architecture through an extensive evaluation using a real-word driving dataset.

This paper explorescriticality-based real-time schedulingof neural-network-based machine inference pipelines in cyber-physical systems (CPS) to mitigate the effect of algorithmic priority inversion. We specifically focus on the perception subsystem, an important subsystem feeding other components (e.g., planning and control). In general, priority inversion occurs in real-time systems when computations that are of lower priority are performed together with or ahead of those that are of higher priority. In current machine perception software, significant priority inversion occurs becauseresource allocationto the underlying neural network models does not differentiate between critical and less critical data within a scene. To remedy this problem, in recent work, we proposed an architecture to partition the input data into regions of different criticality, then formulated a utility-based optimization problem to batch and schedule their processing in a manner that maximizes confidence in perception results, subject to criticality-based time constraints. This journal extension matures the work in several directions: (i) We extend confidence maximization to a generalized utility optimization formulation that accounts for criticality in the utility function itself, offering finer-grained control over resource allocation within the perception pipeline; (ii) we further instantiate and compare two different criticality metrics (distance-based and relative velocity-based) to understand their relative advantages; and (iii) we explore the limitations of the approach, specifically how inaccuracies in criticality-based attention cueing affect performance. All experiments are conducted on the NVIDIA Jetson AGX Xavier platform with a real-world driving dataset.

Network Utility Maximization (NUM) studies the problems of allocating traffic rates to network users in order to maximize the users’ total utility subject to network resource constraints. In this paper, we propose a new NUM framework, Learning-NUM, where the users’ utility functions are unknown apriori and the utility function values of the traffic rates can be observed only after the corresponding traffic is delivered to the destination, which means that the utility feedback experiences queueing delay. The goal is to design a policy that gradually learns the utility functions and makes rate allocation and network scheduling/routing decisions so as to maximize the total utility obtained over a finite time horizon$T$. In addition to unknown utility functions and stochastic constraints, a central challenge of our problem lies in the queueing delay of the observations, which may be unbounded and depends on the decisions of the policy. We first show that the expected total utility obtained by the best dynamic policy is upper bounded by the solution to a static optimization problem. Without the presence of feedback delay, we design an algorithm based on the ideas of gradient estimation and Max-Weight scheduling. To handle the feedback delay, we embed the algorithm in a parallel-instance paradigm to form a policy that achieves$\tilde {O}(T^{3/4})$-regret, i.e., the difference between the expected utility obtained by the best dynamic policy and our policy is in$\tilde {O}(T^{3/4})$. Furthermore, we extend our policy to deal with the case where the utility observations are noisy and show that it achieves$\tilde {O}(T^{7/8})$-regret. Finally, to demonstrate the practical applicability of the Learning-NUM framework, we apply it to three application scenarios including database query, job scheduling and video streaming. We further conduct simulations on the job scheduling application to evaluate the empirical performance of our policy.

Network Utility Maximization (NUM) studies the problems of allocating traffic rates to network users in order to maximize the users' total utility subject to network resource constraints. In this paper, we propose a new NUM framework, Learning-NUM, where the users' utility functions are unknown apriori and the utility function values of the traffic rates can be observed only after the corresponding traffic is delivered to the destination, which means that the utility feedback experiences queueing delay. The goal is to design a policy that gradually learns the utility functions and makes rate allocation and network scheduling/routing decisions so as to maximize the total utility obtained over a finite time horizon T. In addition to unknown utility functions and stochastic constraints, a central challenge of our problem lies in the queueing delay of the observations, which may be unbounded and depends on the decisions of the policy. We first show that the expected total utility obtained by the best dynamic policy is upper bounded by the solution to a static optimization problem. Without the presence of feedback delay, we design an algorithm based on the ideas of gradient estimation and Max-Weight scheduling. To handle the feedback delay, we embed the algorithm in a parallel-instance paradigm to form a policy that achieves Õ(T3/4)-regret, i.e., the difference between the expected utility obtained by the best dynamic policy and our policy is in Õ(T3/4). Finally, to demonstrate the practical applicability of the Learning-NUM framework, we apply it to three application scenarios including database query, job scheduling and video streaming. We further conduct simulations on the job scheduling application to evaluate the empirical performance of our policy.

The paper discusses algorithmic priority inversion in mission-critical machine inference pipelines used in modern neural-network-based cyber-physical applications, and develops a scheduling solution to mitigate its effect. In general, priority inversion occurs in real-time systems when computations that are of lower priority are performed together with or ahead of those that are of higher priority.1In current machine intelligence software, significant priority inversion occurs on the path from perception to decision-making, where the execution of underlying neural network algorithms does not differentiate between critical and less critical data. We describe a scheduling framework to resolve this problem, and demonstrate that it improves the system’s ability to react to critical inputs, while at the same time reducing platform cost.

Large volumes of event data are becoming increasingly available on online social networks. These events are usually causally dependent to each other, reflecting the interactions and collaborations among different parties. Learning and interpreting the temporal patterns and dynamics within these event streams plays an important role in many practical applications, such as trend prediction and anomaly detection. Since causal dependencies can be reflected in both event time (i.e., when) and event content (i.e., who and what), we thus develop a user community based generative model, called latent Hawkes process (LHP), taking into account both-side information to illustrate the generation of such inter-dependent event streams on GitHub repositories, where each attribute is assumed to be generated by interplays between correlated latent communities. Through learning of our model, two functionalities are fulfilled concurrently: event clustering (i.e., community discovery) and temporal dependency learning among these clusters (i.e., dependency profiling). To do so, we design an EM-based framework integrating sequential Monte Carlo sampling to estimate model parameters in an end-to-end manner. Through experiments on practical GitHub event data, we validate the effectiveness of LHP in extracting user community structures and learning their correlated temporal dynamics. Such knowledge further enables us to gain new insights into the development status of software, such as the project persistence and anomaly detection.

Traditional network interdiction refers to the problem of an interdictor trying to reduce the throughput of network users by removing network edges. In this paper, we propose a new paradigm for network interdiction that models scenarios, such as stealth DoS attack, where the interdiction is performed through injecting adversarial traffic flows. Under this paradigm, we first study the deterministic flow interdiction problem, where the interdictor has perfect knowledge of the operation of network users. We show that the problem is highly inapproximable on general networks and is NP-hard even when the network is acyclic. We then propose an algorithm that achieves a logarithmic approximation ratio and quasi-polynomial time complexity for acyclic networks through harnessing the submodularity of the problem. Next, we investigate the robust flow interdiction problem, which adopts the robust optimization framework to capture the case where definitive knowledge of the operation of network users is not available. We design an approximation framework that integrates the aforementioned algorithm, yielding a quasi-polynomial time procedure with poly-logarithmic approximation ratio for the more challenging robust flow interdiction. Finally, we evaluate the performance of the proposed algorithms through simulations, showing that they can be efficiently implemented and yield near-optimal solutions.

In many real-world networks, entities of different types usually form an evolving network with hybrid interactions. However, how to theoretically model such networks, along with quantitive characterizations, remains unexplored. Motivated by this, we develop a novel evolving model, which, as validated by our empirical results, can well capture some basic properties such as power-law degree distribution, densification, shrinking diameter, and community structure embodied in most real datasets. Particularly, two types of results are presented in this paper. First, our proposed model, namely, evolving K-Graph, consists of K-node sets representing K different types of entities. The hybrid interactions among entities, based on whether they belong to the same type, are classified into inter-type and intra-type ones that are, respectively, characterized by two joint graphs evolving over time. Following our newly proposed mechanism called interactive-evolution, potential connections can be established among nodes with common features and further form a positive feedback. The superiorities of our model are three folded: good capture of realistic networks, mathematical tractability and efficient implementation. Second, by analytical derivations, along with empirical validation on real datasets, we disclose two aspects of network properties: basic ones as power-law degree distribution, densification, shrinking diameter and community structure, as well as a distinctive one, that is, positive correlation observed in real networks, implying that a hub in one inter-type relationship network also has many neighbors in another one. An additional interesting finding is that through further comparison of models with or without interactive-evolution, the former one leads to an even earlier occurrence of network connectivity.

The advent of social networks poses severe threats on user privacy as adversaries can de-anonymize users' identities by mapping them to correlated cross-domain networks. Without ground-truth mapping, prior literature proposes various cost functions in hope of measuring the quality of mappings. However, there is generally a lacking of rationale behind the cost functions, whose minimizer also remains algorithmically unknown. We jointly tackle above concerns under a more practical social network model parameterized by overlapping communities, which, neglected by prior art, can serve as side information for de-anonymization. Regarding the unavailability of ground-truth mapping to adversaries, by virtue of the Minimum Mean Square Error (MMSE), our first contribution is a well-justified cost function minimizing the expected number of mismatched users over all possible true mappings. While proving the NP-hardness of minimizing MMSE, we validly transform it into the weighted-edge matching problem (WEMP), which, as disclosed theoretically, resolves the tension between optimality and complexity: (i) WEMP asymptotically returns a negligible mapping error in large network size under mild conditions facilitated by higher overlapping strength; (ii) WEMP can be algorithmically characterized via the convex-concave based de-anonymization algorithm (CBDA), finding the optimum of WEMP. Extensive experiments further confirm the effectiveness of CBDA under overlapping communities, in terms of averagely 90% re-identified users in the rare true cross-domain co-author networks when communities overlap densely, and roughly 70% enhanced reidentification ratio compared to non-overlapping cases.

This paper studies the problem of optimizing multicast energy consumption in delay-constrained mobile wireless networks, where information from the source needs to be delivered to all the k destinations within an imposed delay constraint. Most existing works simply focus on deriving transmission schemes with the minimum transmitting energy, overlooking the energy consumption at the receiver side. Therefore, in this paper, we propose ConMap, a novel and general framework for efficient transmission scheme design that jointly optimizes both the transmitting and receiving energy. In doing so, we formulate our problem of designing minimum energy transmission scheme, called DeMEM, as a combinatorial optimization one, and prove that the approximation ratio of any polynomial time algorithm for DeMEM cannot be better than (1/4) lnk. Aiming to provide more efficient approximation schemes, the proposed ConMap first converts DeMEM into an equivalent directed Steiner tree problem through creating auxiliary graph gadgets to capture energy consumption, then maps the computed tree back into a transmission scheme. The advantages of ConMap are threefolded: 1) Generality- ConMap exhibits strong applicability to a wide range of energy models; 2) Flexibility- Any algorithm designed for the problem of directed Steiner tree can be embedded into our ConMap framework to achieve different performance guarantees and complexities; 3) Efficiency- ConMap preserves the approximation ratio of the embedded Steiner tree algorithm, to which only slight overhead will be incurred. The three features are then empirically validated, with ConMap also yielding near-optimal transmission schemes compared to a brute-force exact algorithm. To our best knowledge, this is the first work that jointly considers both the transmitting and receiving energy in the design of multicast transmission schemes in mobile wireless networks.

Location-aware viral marketing is crucial in modern commercial applications for attracting customers to certain points of interests. Prior works are mainly based on formulating it into a location-aware influence maximization problem in Geo-social Networks (GSNs), where $K$ initial seed individuals are selected in hope of maximizing the number of final influenced users. In this paper, we present the first look into the group-level location promotion, which can potentially enhance its performance, with the phenomenon that users belonging to the same geo-community share similar moving preferences. We propose GLP, a new and novel framework of group-level location promotion by virtue of geo-communities, each of which is treated as a group in GSNs. Aiming to attract more users to designated locations, GLP firstly carries out user grouping through an iterative learning approach based on information extraction from massive check-ins records. The advantage of GLP is three-folded: i) by aggregating movements of group members, GLP significantly avoids the sparsity and sporadicity of individual check-ins, and thus obtains more reliable mobility models; ii) by generalizing a new group-level social graph, GLP can exponentially reduce the computational complexity of seed nodes selection that is algorithmically executed by a greedy algorithm; iii) in comparison with prior individual-level cases, GLP is theoretically demonstrated to drastically increase influence spread under the same given budget. Extensive experiments on real datasets demonstrate that the GLP outperforms four baselines, with notably up to 10 times larger influence spread and 100 times faster seed selection over two individual-level cases, meanwhile verifying the impact of group numbers in final influence spread.

A crucial privacy-driven issue nowadays is re- identifying ano-nymized social networks by mapping them to correlated cross-domain auxiliary networks. Prior works are typically based on modeling social networks as random graphs representing users and their relations, and subsequently quantify the quality of mappings through cost functions that are proposed without sufficient rationale. Also, it remains unknown how to algorithmically meet the demand of such quantifications, i.e., to find the minimizer of the cost functions. We address those concerns in a more realistic social network modeling parameterized by community structures that can be leveraged as side information for de- anonymization. By Maximum A Posteriori (MAP) estimation, our first contribution is new and well justified cost functions, which, when minimized, enjoy superiority to previous ones in finding the correct mapping with the highest probability. The feasibility of the cost functions is then for the first time algorithmically characterized. While proving the general multiplicative inapproximability, we are able to propose two heuristics, which, respectively, enjoy an ε-additive approximation and a conditional optimality in carrying out successful user re- identification. Our theoretical findings are empirically validated,with a notable dataset extracted from rare true cross-domain networks that reproduce genuine social network de-anonymization.

Determination of source-destination connectivity in networks has long been a fundamental problem, where most existing works are based on deterministic graphs that overlook the inherent uncertainty in network links. To overcome such limitation, this paper models the network as an uncertain graph where each edge e exists independently with some probability p(e). The problem examined is that of determining whether a given pair of nodes, a source s and a destination t, are connected by a path or separated by a cut. Assuming that during each determining process we are associated with an underlying graph, the existence of each edge can be unraveled through edge testing at a cost of c(e). Our goal is to find an optimal strategy incurring the minimum expected testing cost with the expectation taken over all possible underlying graphs that form a product distribution. Formulating it into a combinatorial optimization problem, we first characterize the computational complexity of optimally determining source-destination connectivity in uncertain graphs. Specifically, through proving the NP-hardness of two closely related problems, we show that, contrary to its counterpart in deterministic graphs, this problem cannot be solved in polynomial time unless P=NP. Driven by the necessity of designing an exact algorithm, we then apply the Markov Decision Process framework to give a dynamic programming algorithm that derives the optimal strategies. As the exact algorithm may have prohibitive time complexity in practical situations, we further propose two more efficient approximation schemes compromising the optimality. The first one is a simple greedy approach with linear approximation ratio. Interestingly, we show that naive as it is, it has comparable performance than some other seemingly more sophisticated algorithms. Second, by harnessing the sub-modularity of the problem, we further design a more elaborate algorithm with better approximation ratio. The effectiveness of the proposed algorithms are justified through extensive simulations on three real network datasets, from which we demonstrate that the proposed algorithms yield strategies with smaller expected cost than conventional heuristics.

This paper studies the problem of optimizing multicast energy consumption in delay-constrained mobile wireless networks, where information from the source needs to be delivered to all the k destinations within an imposed delay constraint. Most existing works simply focus on deriving transmission schemes with the minimum transmitting energy, overlooking the energy consumption at the receiver side. Therefore, in this paper, we propose ConMap, a novel and general framework for efficient transmission scheme design that jointly optimizes both the transmitting and receiving energy. In doing so, we formulate our problem of designing minimum energy transmission scheme, called DeMEM, as a combinatorial optimization one, and prove that the approximation ratio of any polynomial time algorithm for DeMEM cannot be better than ¼ ln k. Aiming to provide more efficient approximation schemes, the proposed ConMap first converts DeMEM into an equivalent directed Steiner tree problem through creating auxiliary graph gadgets to capture energy consumption, then maps the computed tree back into a transmission scheme. The advantages of ConMap are threefolded: i) Generality-- ConMap exhibits strong applicability to a wide range of energy models; ii) Flexibility-- Any algorithm designed for the problem of directed Steiner tree can be embedded into our ConMap framework to achieve different performance guarantees and complexities; iii) Efficiency-- ConMap preserves the approximation ratio of the embedded Steiner tree algorithm, to which only slight overhead will be incurred. The three features are then empirically validated, with ConMap also yielding near-optimal transmission schemes compared to a brute-force exact algorithm. To our best knowledge, this is the first work that jointly considers both the transmitting and receiving energy in the design of multicast transmission schemes in mobile wireless networks.

In many realistic networks, entities of different types usually form an evolving network with hybrid interactions. However, how to mathematically model such networks remains unexplored. Motivated by this, we develop a novel evolving model, which, as validated by our empirical results, can well capture some basic features such as power-law distribution, densification and shrinking diameter. Particularly, in our proposed model, named Evolving K-Graph, the hybrid interactions among entities are classified into inter-type and intra-type connections that are respectively characterized by two joint graphs evolving over time. By empirical validation, we disclose two new network properties: a positive correlation of any two layers of the network, and an earlier occurrence of network connectivity resulted by our model.

Multicast tree is a key structure for data dissemination from one source to multiple receivers in wireless networks. Minimum length multica modeled as the Steiner tree problem, and is proven to be NP-hard. In this paper, we explore how to efficiently generate minimum length multi wireless sensor networks (WSNs), where only limited knowledge of network topology is available at each node. We design and analyze a simple algorithm, which we call toward source tree (TST), to build multicast trees in WSNs. We show three metrics of TST algorithm, i.e., running and energy efficiency. We prove that its running time is O(√(n log n)), the best among all existing solutions to our best knowledge. We prove that TST tree length is in the same order as Steiner tree, which give a theoretical upper bound and use simulations to show the ratio be only 1.114 when nodes are uniformly distributed. We evaluate energy efficiency in terms of message complexity and the number of forwarding prove that they are both order-optimal. We give an efficient way to construct multicast tree in support of transmission of voluminous data.

Determination of source-destination connectivity in networks has long been a fundamental problem, where most existing works are based on deterministic graphs that overlook the inherent uncertainty in network links. To overcome such limitation, this paper models the network as an uncertain graph, where each edge e exists independently with some probability p(e). The problem examined is that of determining whether a given pair of nodes, a source s and a destination t, are connected by a path or separated by a cut. Assuming that during each determining process we are associated with an underlying graph, the existence of each edge can be unraveled through edge testing at a cost of c(e). Our goal is to find an optimal strategy incurring the minimum expected testing cost with the expectation taken over all possible underlying graphs that form a product distribution. Formulating it into a combinatorial optimization problem, we first characterize the computational complexity of optimally determining source-destination connectivity in uncertain graphs. Specifically, through proving the NP-hardness of two closely related problems, we show that, contrary to its counterpart in deterministic graphs, this problem cannot be solved in polynomial time unless P = NP. Driven by the necessity of designing an exact algorithm, we then apply the Markov decision process framework to give a dynamic programming algorithm that derives the optimal strategies. As the exact algorithm may have prohibitive time complexity in practical situations, we further propose two more efficient approximation schemes compromising the optimality. The first one is a simple greedy approach with linear approximation ratio. Interestingly, we show that naive as it is, and it enjoys significantly better performance guarantee than some other seemingly more sophisticated algorithms. Second, by harnessing the submodularity of the problem, we further design a more elaborate algorithm with better approximation ratio. The effectiveness of the proposed algorithms is justified through extensive simulations on three real network data sets, from which we demonstrate that the proposed algorithms yield strategies with smaller expected cost than conventional heuristics.