Distributed optimal self-organisation in a class of wireless sensor networks

Karnik, Aditya; Kumar, Anurag

doi:10.1109/infcom.2004.1354525

Cited by 11 publications

(16 citation statements)

References 38 publications

(21 reference statements)

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“…The idea is to replace a link between nodes and by multiple "artificial links," each one corresponding to a feasible combination of transmit power and modulation. 6 Thus, optimal selection of power and modulation is translated into optimal selection of "links." Since all the feasible links are, thus, given a priori, the conflict structure is fixed, and corresponds to the set of non-conflicting schedules of all "artificial" links.…”

Section: Structure Of the Optimal Routesmentioning

confidence: 99%

“…Clearly, setting for all also results in an optimal solution of (TOPARAM). (4) implies that this is 6 For uniformity of notation, we continue to denote by L (resp. L) the set of all artificial links (resp.…”

Section: ) Lagrange Multipliers Exist For (Toparam)mentioning

confidence: 99%

“…This is an appropriate notion of capacity from a networking perspective, since it can represent the aggregate bandwidth demands of subscriber stations in an IEEE 802.16-like access network, or the sampling rate at which sensors produce information about their environment in a sensor network [6]. It is also the classical notion of capacity à la Gupta-Kumar [1].…”

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confidence: 99%

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Throughput-Optimal Configuration of Fixed Wireless Networks

Karnik

Iyer

Rosenberg

2008

IEEE/ACM Trans. Networking

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Abstract-In this paper, we address the following two questions concerning the capacity and configuration of fixed wireless networks: (i) given a set of wireless nodes with arbitrary but fixed locations, and a set of data flows, what is the max-min achievable throughput? and (ii) how should the network be configured to achieve the optimum? We consider these questions from a networking standpoint assuming point-to-point links, and employ a rigorous physical layer model to model conflict relationships between them. Since we seek capacity results, we assume that the network is operated using an appropriate schedule of conflict-free link activations. We develop and investigate a novel optimization framework to determine the optimal throughput and configuration, i.e., flow routes, link activation schedules and physical layer parameters. Determining the optimal throughput is a computationally hard problem, in general. However, using a smart enumerative technique we obtain numerical results for several different scenarios of interest. We obtain several important insights into the structure of the optimal routes, schedules and physical layer parameters. Besides determining the achievable throughput, we believe that our optimization-based framework can also be used as a tool, for configuring scheduled wireless networks, such as those based on IEEE 802.16.Index Terms-Capacity, fixed wireless networks, IEEE 802.16, mesh networks, optimal scheduling and routing.

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Section: Structure Of the Optimal Routesmentioning

confidence: 99%

Section: ) Lagrange Multipliers Exist For (Toparam)mentioning

confidence: 99%

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confidence: 99%

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Throughput-Optimal Configuration of Fixed Wireless Networks

Karnik

Iyer

Rosenberg

2008

IEEE/ACM Trans. Networking

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“…The functions they consider are symmetric 3 . Further, two subclasses of summetric functions, namely, typesensitive functions and type-threshold functions 4 are considered. Scaling laws for upper and lower bounds on the computation rate are obtained in [2] for these subclasses of functions.…”

Section: Distributed Computation Modelmentioning

confidence: 99%

“…The objective is to collaboratively compute and deliver max{v 1 (k), v 2 (k), · · · , v n (k)} to an operator station, for each such vector of sampled values. See [4] where the need for a distributed maximum computation arises as a part of a distributed self-tuning algorithm for the optimal operation of a sensor network. If the sensors calculate local maxima while routing the values to the operator station, we can reduce the traffic in the network and thereby decrease the computation delay and increase the network lifetime.…”

Section: Introductionmentioning

confidence: 99%

Time and energy complexity of distributed computation in wireless sensor networks

Khude

Kumar

Karnik³

Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies.

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Abstract-We consider a scenario in which a wireless sensor network is formed by randomly deploying n sensors to measure some spatial function over a field, with the objective of computing a function of the measurements and communicating it to an operator station. We restrict ourselves to the class of type-threshold functions (as defined in [2]), of which max, min, and indicator functions are important examples; our discussions are couched in terms of the max function. We view the problem as one of message passing distributed computation over a geometric random graph. The network is assumed to be synchronous; the sensors synchronously measure values, and then collaborate to compute and deliver the function computed with these values to the operator station. Computation algorithms differ in (i) the communication topology assumed, and (ii) the messages that the nodes need to exchange in order to carry out the computation. The focus of our paper is to establish (in probability) scaling laws for the time and energy complexity of the distributed function computation over random wireless networks, under the assumption of centralised contention-free scheduling of packet transmissions. Firstly, without any constraint on the computation algorithm, we establish scaling laws for the computation time and energy expenditure for one time maximum computation. We show that, for an optimal algorithm, the computation time and energy expenditure scale, respectively, as Θ n log n and Θ(n) asymptotically as the number of sensors n → ∞. Secondly, we analyze the performance of three specific computation algorithms that may be used in specific practical situations, namely, the Tree algorithm, Multi-Hop transmission, and the Ripple algorithm (a type of gossip algorithm), and obtain scaling laws for the computation time and energy expenditure as n → ∞. In particular we show that the computation time for these algorithms scales as Θ √ n log n , Θ(n) and Θ √ n log n , respectively; whereas the energy expended scales as Θ(n), Θ n n log n and Θ n √ n log n , respectively. Finally, simulation results are provided to show that our analysis indeed captures the correct scaling; the simulations also yield estimates of the constant multipliers in the scaling laws. Our analyses throughout assume a centralized optimal scheduler and hence our results can be viewed as providing bounds for the performance with practical distributed schedulers.

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