Elsevier

Discrete Applied Mathematics

Volume 164, Part 1, 19 February 2014, Pages 349-355
Discrete Applied Mathematics

A 1-local 4/3-competitive algorithm for multicoloring a subclass of hexagonal graphs

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Abstract

We consider a frequency allocation problem, in which we are given a cellular telephone network whose geographical coverage area is divided into cells in which phone calls are serviced by frequencies assigned to them, so that none of the pairs of calls emanating from the same or neighboring cells is assigned the same frequency. The problem is to use the frequencies efficiently, i.e., to 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 present a 1-local 4/3-competitive distributed algorithm for multicoloring a hexagonal graph without certain forbidden configuration (introduced in Šparl and Žerovnik (2010) [7]).

Keywords

Hexagonal graphs
Multicoloring
Algorithm
Frequency assignment problem
FAP

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