# A branch & cut algorithm for the minimum-adjacency vertex coloring problem

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 representing the potential interference between the antennas and a set of prespecified colors/channels, asks for a vertex coloring of 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. Lien vers l'article

DELLE DONNE, D. and MARENCO, J. (2011). A branch & cut algorithm for the minimum-adjacency vertex coloring problem. *Discrete Optimization*, 8(4), pp. 540-554.

Mots clés : #Frequency-assignment, #Adjacent-colors, #Integer-programming