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Approximating Minimum Power Edge-Multi-Covers

  • Nachshon Cohen
  • Zeev Nutov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7353)

Abstract

Given a graph with edge costs, the power of a node is the maximum cost of an edge incident to it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider the following fundamental problem in wireless network design. Given a graph G = (V,E) with edge costs and degree bounds {r(v):v ∈ V}, the Minimum-Power Edge-Multi-Cover (MPEMC) problem is to find a minimum-power subgraph J of G such that the degree of every node v in J is at least r(v). Let k =  max v ∈ V r(v). For k = Ω(logn), the previous best approximation ratio for MPEMC was O(logn), even for uniform costs [3]. Our main result improves this ratio to O(logk) for general costs, and to O(1) for uniform costs. This also implies ratios O(logk) for the Minimum-Power k -Outconnected Subgraph and \(O\left(\log k \log \frac{n}{n-k} \right)\) for the Minimum-Power k -Connected Subgraph problems; the latter is the currently best known ratio for the min-cost version of the problem. In addition, for small values of k, we improve the previously best ratio k + 1 to k + 1/2.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Nachshon Cohen
    • 1
  • Zeev Nutov
    • 1
  1. 1.The Open University of IsraelIsrael

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