2-Local 5/4-competitive algorithm for multicoloring triangle-free hexagonal graphs

  • Authors:

  • Petra Šparl;Janez Žerovnik

  • Affiliations:

  • Faculty of Civil Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia and Institute of Mathematics, Physics and Mechanics, Jadranska 19, Department of Theoretical Computer Scie ...;Institute of Mathematics, Physics and Mechanics, Jadranska 19, Department of Theoretical Computer Science, 1111 Ljubljana, Slovenia and Faculty of Mechanical Engineering, University of Maribor, Sm ...

  • Venue:
  • Information Processing Letters
  • Year:
  • 2004

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Abstract

An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular network is generally modeled as a subgraph of the infinite triangular lattice. The distributed frequency assignment problem can be abstracted as a multicoloring problem on a weighted hexagonal graph, where the weight vector represents the number of calls to be assigned at vertices. In this paper we present a 2-local distributed algorithm for multicoloring triangle-free hexagonal graphs using only the local clique numbers ω1 (υ) and ω2(υ) at each vertex υ of the given hexagonal graph, which can be computed from local information available at the vertex. We prove that the algorithm uses no more than [5ω(G)/4] + 3 colors for any triangle-free hexagonal graph G, without explicitly computing the global clique number ω(G). Hence the competitive ratio of the algorithm is 5/4.