Abstract
In this work we study a particular way of dealing with interference in combinatorial optimization models representing wireless communication networks. In a typical wireless network, co-channel interference occurs whenever two overlapping antennas use the same frequency channel, and a less critical interference is generated whenever two overlapping antennas use adjacent channels. This motivates the formulation of the minimum-adjacency vertex coloring problem which, given an interference graph G representing the potential interference between the antennas and a set of prespecified colors/channels, asks for a vertex coloring of G minimizing the number of edges receiving adjacent colors. We propose an integer programming model for this problem and present three families of facet-inducing valid inequalities. Based on these results, we implement a branch-and-cut algorithm for this problem, and we provide promising computational results.
Highlights
We are interested in a combinatorial optimization problem arising from frequency assignment problems in wireless communication networks, that was motivated by the types of interference generated in GSM mobile phone networks [1]
We have performed a polyhedral study of an integer programming formulation for this problem, presenting three facet-inducing families of valid inequalities
The instances we are able to solve to optimality are far from being real-size instances, we believe that the results presented in this work may contribute to future developments for the practical solution of frequency assignment problems
Summary
We are interested in a combinatorial optimization problem arising from frequency assignment problems in wireless communication networks, that was motivated by the types of interference generated in GSM mobile phone networks [1]. We are interested in the polyhedral structure generated by such a combinatorial optimization problem, which includes a graph coloring structure with additional considerations on adjacent channels/colors. Based on these observations, we introduce in this work the minimumadjacency vertex coloring problem, present an initial polyhedral study and, based on these results, implement a branch-andcut algorithm for this problem.
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