1‐Local 7/5‐Competitive Algorithm for Multicoloring Hexagonal Graphs

1‐Local 7/5‐Competitive Algorithm for Multicoloring Hexagonal Graphs

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Article ID: iaor20126445
Volume: 64
Issue: 4
Start Page Number: 564
End Page Number: 583
Publication Date: Dec 2012
Journal: Algorithmica
Authors: , ,
Keywords: allocation: resources
Abstract:

In the frequency allocation problem, we are given a cellular telephone network whose geographical coverage area is divided into cells, where 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. minimize the span of frequencies used. The frequency allocation problem can be regarded as a multicoloring problem on a weighted hexagonal graph, where every vertex knows its position in the graph. We present a 1‐local 7/5‐competitive distributed algorithm for multicoloring a hexagonal graph, thereby improving the previous 1‐local 17/12‐competitive algorithm.

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