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Bounded-Hop Energy-Efficient Broadcast in Low-Dimensional Metrics Via Coresets

  • Stefan Funke
  • Sören Laue
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)

Abstract

We consider the problem of assigning powers to nodes of a wireless network in the plane such that a message from a source node s reaches all other nodes within a bounded number k of transmissions and the total amount of assigned energy is minimized. By showing the existence of a coreset of size \(O(\left({{1}\over{\epsilon}}\right)^{4k})\) we are able to (1 + ε)-approximate the bounded-hop broadcast problem in time linear in n which is a drastic improvement upon the previously best known algorithm.

While actual network deployments often are in a planar setting, the experienced metric for several reasons is typically not exactly of the Euclidean type, but in some sense ’close’. Our algorithm (and others) also work for non-Euclidean metrics provided they exhibit a certain similarity to the Euclidean metric which is known in the literature as bounded doubling dimension. We give a novel characterization of such metrics also pointing out other applications such as space-efficient routing schemes.

Keywords

Source Node Voronoi Cell Doubling Dimension Unweighted Graph Range Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Stefan Funke
    • 1
  • Sören Laue
    • 1
  1. 1.Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 SaarbrückenGermany

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