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Minimum Energy Broadcast and Disk Cover in Grid Wireless Networks

(Extended Abstract)
  • Tiziana Calamoneri
  • Andrea E. F. Clementi
  • Miriam Di Ianni
  • Massimo Lauria
  • Angelo Monti
  • Riccardo Silvestri
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4056)

Abstract

The Minimum Energy Broadcast problem consists in finding the minimum-energy range assignment for a given set S of n stations of an ad hoc wireless network that allows a source station to perform broadcast operations over S.

We prove a nearly tight asymptotical bound on the optimal cost for the Minimum Energy Broadcast problem on square grids. We emphasize that finding tight bounds for this problem restriction is far to be easy: it involves the Gauss’s Circle problem and the Apollonian Circle Packing. We also derive near-tight bounds for the Bounded-Hop version of this problem. Our results imply that the best-known heuristic, the MST-based one, for the Minimum Energy Broadcast problem is far to achieve optimal solutions (even) on very regular, well-spread instances: its worst-case approximation ratio is about π and it yields \(\Omega(\sqrt{n})\) hops.

As a by product, we get nearly tight bounds for the Minimum Disk Cover problem and for its restriction in which the allowed disks must have non-constant radius.

Finally, we emphasize that our upper bounds are obtained via polynomial time constructions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tiziana Calamoneri
    • 2
  • Andrea E. F. Clementi
    • 1
  • Miriam Di Ianni
    • 1
  • Massimo Lauria
    • 2
  • Angelo Monti
    • 2
  • Riccardo Silvestri
    • 2
  1. 1.Dipartimento di MatematicaUniversità degli Studi di Roma“Tor Vergata” 
  2. 2.Dipartimento di InformaticaUniversità degli Studi di Roma “La Sapienza” 

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