Approximation algorithms for minimum span channel assignment problems

  • Authors:

  • Yuichiro Miyamoto;Tomomi Matsui

  • Affiliations:

  • Sophia University, Tokyo, Japan;The University of Tokyo, Tokyo, Japan

  • Venue:
  • AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2006

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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.