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Approximation Algorithms for Minimum Span Channel Assignment Problems

  • Yuichiro Miyamoto
  • Tomomi Matsui
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4041)

Abstract

We propose polynomial time approximation algorithms for minimum span channel (frequency) assignment problems, which is known to be NP-hard. Let α be the approximation ratio of our algorithm and W ≥2 be the maximum of numbers of channels required in vertices. If an instance is defined on a perfect graph G, then \(\alpha \leq 1+(1+\frac{1}{W-1})\text{H}_{\omega(G)}\), where \(\text{H}_i\) denotes the i-th harmonic number. For any instance defined on a unit disk graph G, α is less than or equal to \((1+\frac{1}{W-1})(3\text{H}_{\omega(G)}-1)\). If a given graph is 4 or 3 colorable, α is bounded by \((2.5+\frac{1.5}{W-1})\) and \((2+\frac{1}{W-1})\), respectively. We also discuss well-known practical instances called Philadelphia instances and propose an algorithm with α≤12/5.

Keywords

Polynomial Time Approximation Ratio Channel Assignment Perfect Graph Vertex Weight 
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-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yuichiro Miyamoto
    • 1
  • Tomomi Matsui
    • 2
  1. 1.Sophia UniversityTokyoJapan
  2. 2.The University of TokyoTokyoJapan

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