A 1-local 13/9-competitive algorithm for multicoloring hexagonal graphs

  • Authors:

  • Francis Y. L. Chin;Yong Zhang;Hong Zhu

  • Affiliations:

  • Department of Computer Science, The University of Hong Kong, Hong Kong;Department of Computer Science, The University of Hong Kong, Hong Kong;Institute of Theoretical Computing, East China Normal University, China

  • Venue:
  • COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
  • Year:
  • 2007

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Abstract

In the frequency allocation problem, we are given a mobile telephone network, whose geographical coverage area is divided into cells, wherein phone calls are serviced by assigning frequencies to them so that no two calls emanating from the same or neighboring cells are assigned the same frequency. The problem is to use the frequencies efficiently, i.e., minimize the span of frequencies used. The frequency allocation problem can be regarded as a multicoloring problem on a weighted hexagonal graph. In this paper, we give a 1-local 4/3-competitive distributed algorithm for multicoloring a triangle-free hexagonal graph, which is a special case. Based on this result, we then propose a 1-local 13/9-competitive algorithm for multicoloring the (general-case) hexagonal graph, thereby improving the previous 1-local 3/2-competitive algorithm.