A 1-Local Asymptotic 13/9-Competitive Algorithm for Multicoloring Hexagonal Graphs

Authors:
Yong Zhang;Francis Y. L. Chin;Hong Zhu
Affiliations:
The University of Hong Kong, Department of Computer Science, Hong Kong, Hong Kong;The University of Hong Kong, Department of Computer Science, Hong Kong, Hong Kong;East China Normal University, Institute of Theoretical Computing, Shanghai, China
Venue:
Algorithmica
Year:
2009

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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 asymptotic 4/3-competitive distributed algorithm for multicoloring a triangle-free hexagonal graph, which is a special case of hexagonal graph. Based on this result, we then propose a 1-local asymptotic13/9-competitive algorithm for multicoloring the (general-case) hexagonal graph, thereby improving the previous 1-local 3/2-competitive algorithm.