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With the availability of multiple unlicensed spectral bands, and potential cost-based limitations on the capabilities of individual nodes, it is increasingly relevant to study the performance of multichannel wireless networks with channel switching constraints. To this effect, some constraint models have been recently proposed, and connectivity and capacity results have been formulated for networks of randomly deployed single-interface nodes subject to these constraints. One of these constraint models is termed random (c, f) assignment, wherein each node is pre-assigned a random subset of f channels out of c (each having bandwidth W c), and may only switch on these. Previous results for this model established bounds on network capacity, and proved that when c = O(logn), the per-prnd f flow capacity is O(W nlogn) and Ω(W cnlogn) (where prnd = 1 −(1 − f f f f 2 c)(1 − c−1)...(1 − c − f+1) ≥ 1 − e − c). In this paper we present a lower bound construction that matches the previous upper prnd bound. This establishes the capacity as Θ(W nlogn). The surprising implication of this result is that when f = Ω ( √ c), random (c, f) assignment yields capacity of the same order as attainable via unconstrained switching. The routing/scheduling procedure used by us to achieve capacity requires synchronized route-construction for all flows in the network, leading to the open question of whether it is possible to achieve capacity using asynchronous procedures.

We present a general framework for discriminative estimation based on the maximum entropy principle and its extensions. All calculations involve distributions over structures and/or parameters rather than specific settings and reduce to relative entropy projections. This holds even when the data is not separable within the chosen parametric class, in the context of anomaly detection rather than classification, or when the labels in the training set are uncertain or incomplete. Support vector machines are naturally subsumed under this class and we provide several extensions. We are also able to estimate exactly and efficiently discriminative distributions over tree structures of class-conditional models within this framework. Preliminary experimental results are indicative of the potential in these techniques.

This paper describes the mixtures-of-trees model, a probabilistic model for discrete multidimensional domains. Mixtures-of-trees generalize the probabilistic trees of Chow and Liu [6] in a different and complementary direction to that of Bayesian networks. We present efficient algorithms for learning mixtures-of-trees models in maximum likelihood and Bayesian frameworks. We also discuss additional efficiencies that can be obtained when data are “sparse, ” and we present data structures and algorithms that exploit such sparseness. Experimental results demonstrate the performance of the model for both density estimation and classification. We also discuss the sense in which tree-based classifiers perform an implicit form of feature selection, and demonstrate a resulting insensitivity to irrelevant attributes.

Topology control problems are concerned with the assignment of power values to the nodes of an ad~hoc network so that the power assignment leads to a graph topology satisfying some specified properties. This paper considers such problems under several optimization objectives, including minimizing the maximum power and minimizing the total power. A general approach leading to a polynomial algorithm is presented for minimizing maximum power for a class of graph properties called monotone properties. The difficulty of generalizing the approach to properties that are not monotone is discussed. Problems involving the minimization of total power are known to be NP-complete even for simple graph properties. A general approach that leads to an approximation algorithm for minimizing the total power for some monotone properties is presented. Using this approach, a new approximation algorithm for the problem of minimizing the total power for obtaining a 2-node-connected graph is obtained. It is shown that this algorithm provides a constant performance guarantee. Experimental results from an implementation of the approximation algorithm are also presented.

When a sensor network is deployed to detect objects penetrating a protected region, it is not necessary to have every point in the deployment region covered by a sensor. It is enough if the penetrating objects are detected at some point in their trajectory. If a sensor network guarantees that every penetrating object will be detected by at least £ distinct sensors before it crosses the barrier of wireless sensors, we say the network provides £-barrier coverage. In this paper, we develop theoretical foundations for £-barrier coverage. We propose efficient algorithms using which one can quickly determine, after deploying the sensors, whether the deployment region is £-barrier covered. Next, we establish the optimal deployment pattern to achieve £-barrier coverage when deploying sensors deterministically. Finally, we consider barrier coverage with high probability when sensors are deployed randomly. The major challenge, when dealing with probabilistic barrier coverage, is to derive critical conditions using which one can compute the minimum number of sensors needed to ensure barrier coverage with high probability. Deriving critical conditions for £-barrier coverage is, however, still an open problem. We derive critical conditions for a weaker notion of barrier coverage, called weak £-barrier coverage.

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics and function of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements organized into classes. Special attention is given to relating complex network analysis with the areas of pattern recognition and feature selection, as well as on surveying some concepts and measurements from traditional graph theory which are potentially useful for complex network research. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the

We can control the topology of a multi-hop wireless network by varying the transmission power at each node. The life-time of such networks depends on battery power at each node. This paper presents a distributed fault-tolerant topology control algorithm for minimum energy consumption in these networks. More precisely, we present algorithms which preserve the connectivity of a network upon failing of, at most, k nodes (k is constant) and simultaneously minimize the transmission power at each node to some extent. In addition, we present simulations to support the effectiveness of our algorithm. We also demonstrate some optimizations to further minimize the power at each node. Finally, we show how our algorithms can be extended to 3-dimensions.

Compressed sensing is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. In this paper we introduce a new theory for distributed compressed sensing (DCS) that enables new distributed coding algorithms for multi-signal ensembles that exploit both intra- and inter-signal correlation structures. The DCS theory rests on a new concept that we term the joint sparsity of a signal ensemble. We study in detail three simple models for jointly sparse signals, propose algorithms for joint recovery of multiple signals from incoherent projections, and characterize theoretically and empirically the number of measurements per sensor required for accurate reconstruction. We establish a parallel with the Slepian-Wolf theorem from information theory and establish upper and lower bounds on the measurement rates required for encoding jointly sparse signals. In two of our three models, the results are asymptotically best-possible, meaning that both the upper and lower bounds match the performance of our practical algorithms. Moreover, simulations indicate that the asymptotics take effect with just a moderate number of signals. In some sense DCS is a framework for distributed compression of sources with memory, which has remained a challenging problem for some time. DCS is immediately applicable to a range of problems in sensor networks and arrays.