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International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 226-237 | Cite as

The Min-max Edge q-Coloring Problem

  • Tommi Larjomaa
  • Alexandru PopaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)

Abstract

In this paper we introduce and study a new problem named min-max edge q -coloring which is motivated by applications in wireless mesh networks. The input of the problem consists of an undirected graph and an integer q. The goal is to color the edges of the graph with as many colors as possible such that: (a) any vertex is incident to at most q different colors, and (b) the maximum size of a color group (i.e. set of edges identically colored) is minimized. We show the following results:
  1. 1.

    Min-max edge q-coloring is NP-hard, for any \(q \ge 2\).

     
  2. 2.

    A polynomial time exact algorithm for min-max edge q-coloring on trees.

     
  3. 3.

    Exact formulas of the optimal solution for cliques.

     
  4. 4.

    An approximation algorithm for planar graphs.

     

Notes

Acknowledgements

We would like to thank anonymous reviewers for their useful comments.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Communications and NetworkingAalto University School of Electrical EngineeringAaltoFinland
  2. 2.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

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