Approximation algorithm for maximum edge coloring

  • Authors:

  • Wangsen Feng;Liang Zhang;Hanpin Wang

  • Affiliations:

  • Key Laboratory of Network and Software Security Assurance, Computing Center, Peking University, Ministry of Education, Beijing 100871, China;Key Laboratory of High Confidence Software Technologies, School of Electronic Engineering and Computer Science, Peking University, Ministry of Education, Beijing 100871, China;Key Laboratory of High Confidence Software Technologies, School of Electronic Engineering and Computer Science, Peking University, Ministry of Education, Beijing 100871, China

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

Quantified Score

Hi-index 5.23

Visualization

Abstract

We propose a polynomial time approximation algorithm for a novel maximum edge coloring problem which arises from wireless mesh networks [Ashish Raniwala, Tzi-cker Chiueh, Architecture and algorithms for an IEEE 802.11-based multi-channel wireless mesh network, in: INFOCOM 2005, pp. 2223-2234; Ashish Raniwala, Kartik Gopalan, Tzi-cker Chiueh, Centralized channel assignment and routing algorithms for multi-channel wireless mesh networks, Mobile Comput. Commun. Rev. 8 (2) (2004) 50-65]. The problem is to color all the edges in a graph with maximum number of colors under the following q-Constraint: for every vertex in the graph, all the edges incident to it are colored with no more than q (q@?Z,q=2) colors. We show that the algorithm is a 2-approximation for the case q=2 and a (1+4q-23q^2-5q+2)-approximation for the case q2 respectively. The case q=2 is of great importance in practice. For complete graphs and trees, polynomial time accurate algorithms are found for them when q=2. The approximation algorithm gives a feasible solution to channel assignment in multi-channel wireless mesh networks.