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On the Bounded-Hop Range Assignment Problem

  • Paz Carmi
  • Lilach Chaitman-Yerushalmi
  • Ohad Trabelsi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9214)

Abstract

We study the problem of assigning transmission ranges to radio stations in the plane such that any pair of stations can communicate within a bounded number of hops h and the cost of the network is minimized. The cost of transmitting in a range r is proportional to \(r^{\alpha }\), where \(\alpha \ge 1\).

We consider two settings of this problem: collinear station locations and arbitrary locations. For the case of collinear stations, we introduce the pioneer polynomial-time exact algorithm for any \(\alpha \ge 1\) and constant h, and thus conclude that the 1D version of the problem, where h is a constant, is in P. For an arbitrary h, not necessarily a constant, and \(\alpha =1\), we propose a 1.5-approximation algorithm. This improves the previously best known approximation ratio of 2.

For the case of stations placed arbitrarily in the plane, we present a \((6+ \epsilon )\)-approximation algorithm, for any \(\epsilon >0\). This improves the previously best known approximation ratio of \(4(9^{h-2})/(\root h \of {2}-1)\). Moreover, we show a \((1.5+ \epsilon )\)-approximation algorithm for a case where deviation of one hop (\(h+1\) hops in total) is acceptable.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Paz Carmi
    • 1
  • Lilach Chaitman-Yerushalmi
    • 1
  • Ohad Trabelsi
    • 1
  1. 1.Department of Computer ScienceBen-Gurion University of the NegevBeershebaIsrael

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