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Lower bounds and a tabu search algorithm for the minimum deficiency problem

Author

Listed:
  • Mathieu Bouchard

    (École Polytechnique de Montréal and GERAD)

  • Alain Hertz

    (École Polytechnique de Montréal and GERAD)

  • Guy Desaulniers

    (École Polytechnique de Montréal and GERAD)

Abstract

An edge coloring of a graph G=(V,E) is a function c:E→ℕ that assigns a color c(e) to each edge e∈E such that c(e)≠c(e′) whenever e and e′ have a common endpoint. Denoting S v (G,c) the set of colors assigned to the edges incident to a vertex v∈V, and D v (G,c) the minimum number of integers which must be added to S v (G,c) to form an interval, the deficiency D(G,c) of an edge coloring c is defined as the sum ∑ v∈V D v (G,c), and the span of c is the number of colors used in c. The problem of finding, for a given graph, an edge coloring with a minimum deficiency is NP-hard. We give new lower bounds on the minimum deficiency of an edge coloring and on the span of edge colorings with minimum deficiency. We also propose a tabu search algorithm to solve the minimum deficiency problem and report experiments on various graph instances, some of them having a known optimal deficiency.

Suggested Citation

  • Mathieu Bouchard & Alain Hertz & Guy Desaulniers, 2009. "Lower bounds and a tabu search algorithm for the minimum deficiency problem," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 168-191, February.
    • Handle: RePEc:spr:jcomop:v:17:y:2009:i:2:d:10.1007_s10878-007-9106-0
    DOI: 10.1007/s10878-007-9106-0
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