# The Proportional Colouring Problem: Optimizing Buffers in Radio Mesh Networks

1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : In this paper, we consider a new edge colouring problem: the proportional edge-colouring. Given a graph $G$ with positive weights associated to its edges, we want to find a colouring which preserves the proportion given by the weights associated to each edge. If such colouring exists, we want to find one using a minimum number of colours. We proved that deciding if a weighted graph admits a proportional colouring is polynomial while determining its proportional chromatic index is NP-hard. In addition, we give a lower bound and an upper bound for this parameter that can be computed in polynomial time. We finally show a class of graphs and a class of weighted graphs for which we can exactly determine the proportional chromatic index.
Document type :
Conference papers
Domain :

Cited literature [7 references]

https://hal.archives-ouvertes.fr/hal-00429822
Contributor : Hervé Rivano <>
Submitted on : Wednesday, November 4, 2009 - 3:57:14 PM
Last modification on : Monday, November 5, 2018 - 3:36:03 PM
Document(s) archivé(s) le : Thursday, June 17, 2010 - 5:50:39 PM

### File

HLR07.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00429822, version 1

### Citation

Florian Huc, Claudia Linhares Sales, Hervé Rivano. The Proportional Colouring Problem: Optimizing Buffers in Radio Mesh Networks. The IV Latin-American Algorithms, Graphs, and Optimization Symposium (LAGOS 07), Feb 2008, Puerto Varas, Chile. pp.141--146. ⟨hal-00429822⟩

Record views