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Convergence of distributed WSN algorithms: The wake-up scattering problem. (English) Zbl 1237.90105
Majumdar, Rupak (ed.) et al., Hybrid systems: Computation and control. 12th international conference, HSCC 2009, San Francisco, CA, USA, April 13–15, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-00601-2/pbk). Lecture Notes in Computer Science 5469, 180-193 (2009).
Summary: In this paper, we analyze the problem of finding a periodic schedule for the wake-up times of a set of nodes in a wireless sensor network that optimizes the coverage of the region the nodes are deployed on. An exact solution of the problem entails the solution of an integer linear program and is hardly viable on low power nodes. A. Giusti, A. L. Murphy and G. P. Picco [“Decentralized scattering of wake-up times in wireless sensor networks”, Lect. Notes Comput. Sci. 4373, 245–260 (2007)] have recently proposed an efficient decentralized approach that produces a generally good suboptimal solution. In this paper, we study the convergence of this algorithm by casting the problem into one of asymptotic stability for a particular class of linear switching systems. For general topologies of the WSN, we offer local stability results. In some specific special cases, we are also able to prove global stability properties.
For the entire collection see [Zbl 1161.93001].
##### MSC:
 90B36 Stochastic scheduling theory in operations research 90C59 Approximation methods and heuristics in mathematical programming 93C55 Discrete-time control/observation systems 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory
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