The Proportional Coloring Problem: Optimizing Buffers in Radio Mesh Networks

Florian Huc (1) , Claudia Linhares Sales (2) , Hervé Rivano (3)

1 LPD - Distributed Programming Laboratory
2 ParGO - Parallelism, Graphs and Optimization Research Group
3 URBANET - Réseaux capillaires urbains

In this paper, we consider a new edge coloring problem to model call scheduling op- timization issues in wireless mesh networks: the proportional coloring. It consists in finding a minimum cost edge coloring of a graph which preserves the propor- tion given by the weights associated to each of its edges. We show that deciding if a weighted graph admits a proportional coloring is pseudo-polynomial while de- termining its proportional chromatic index is NP-hard. We then give lower and upper bounds for this parameter that can be computed in pseudo-polynomial time. We finally identify a class of graphs and a class of weighted graphs for which the proportional chromatic index can be exactly determined.

Mots clés: edge coloring; proportional coloring; mesh networks; call scheduling

Domaines: Réseaux et télécommunications [cs.NI]

Florian Huc, Claudia Linhares Sales, Hervé Rivano. The Proportional Coloring Problem: Optimizing Buffers in Radio Mesh Networks. Discrete Mathematics, Algorithms and Applications, 2012. ⟨hal-00657802⟩