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)


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.


Source Node Voronoi Cell Doubling Dimension Unweighted Graph Range Assignment 
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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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