Rafal Witkowski ; Janez Žerovnik - 1-local 33/24-competitive Algorithm for Multicoloring Hexagonal Graphs

dmtcs:614 - Discrete Mathematics & Theoretical Computer Science, November 21, 2013, Vol. 15 no. 3 - https://doi.org/10.46298/dmtcs.614
1-local 33/24-competitive Algorithm for Multicoloring Hexagonal GraphsArticle

Authors: Rafal Witkowski 1; Janez Žerovnik ORCID2

  • 1 Faculty of Mathematics and Computer Science [Poznan]
  • 2 Faculty of Mechanical Engineering [Ljubljana]

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 assigned frequencies, 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 each vertex knows its position in the graph. We present a 1-local 33/24-competitive distributed algorithm for multicoloring a hexagonal graph, thereby improving the previous 1-local 7/5-competitive algorithm.

Volume: Vol. 15 no. 3
Section: Graph Theory
Published on: November 21, 2013
Accepted on: June 9, 2015
Submitted on: May 11, 2012
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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