THE PROPORTIONAL COLORING PROBLEM: OPTIMIZING BUFFERS IN RADIO MESH NETWORKS

Author:

HUC FLORIAN12,SALES CLÁUDIA LINHARES3,RIVANO HERVÉ14

Affiliation:

1. Project Team Mascotte – I3S (CNRS-UNS)/INRIA, Sophia Antipolis, France

2. TCS-Sensor Lab, Computer Science Dept., University of Geneva, Switzerland

3. Universidade Federal do Ceará, Brazil

4. Project Team SWING – INSA Lyon/INRIA, Villeurbanne, France

Abstract

In this paper, we consider a new edge coloring problem to model call scheduling optimization issues in wireless mesh networks: the proportional coloring. It consists in finding a minimum cost edge coloring of a graph which preserves the proportion 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 determining 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Reference15 articles.

1. Wireless mesh networks: a survey

2. Sharing Resources at Nonuniform Access Rates

3. Scheduling to Minimize Interaction Cost

4. G. Frobenius, Sitzungsberichte der KÃ niglich Preussischen Akademie der Wissenschaften zu Berlin (1917) pp. 456–477.

5. The NP-Completeness of Edge-Coloring

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