Improving a Family of Approximation Algorithms to Edge Color Multigraphs

Caprara, Alberto and Rizzi, Romeo (1998) Improving a Family of Approximation Algorithms to Edge Color Multigraphs. UNSPECIFIED.

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    Given a multigraph G=(V,E), the Edge Coloring Problem (ECP) calls for the minimum number X of colors needed to color the edges in E so that all edges incident with a common node are assigned different colors. The best known polynomial time approximation algorithms for ECP belong to a same family, which is likely to contain, for each positive integer k, an algorithm which uses at most ((2k+1)X+(2k-2))/2k (rounded up) colors. For k<= 5 the existence of the corresponding algorithm was shown, whereas for larger values of k the question is open. We show that, for any k such that the corresponding algorithm exists, it is possible to improve the algorithm so as to use at most ((2k+1)X+(2k-3))/2k (rounded up) colors. It is easily shown that the (2k-3)/2k term cannot be reduced further, unless P=NP. We also discuss how our result can be used to extend the set of cases in which well-known conjectures on ECP are valid.

    Item Type: Departmental Technical Report
    Department or Research center: Information Engineering and Computer Science
    Subjects: Q Science > QA Mathematics > QA075 Electronic computers. Computer science
    Uncontrolled Keywords: Edge Coloring, Approximation Algorithm, Matching
    Additional Information: Published in "Inf. Proc. Lett.", vol. 68 (1998) 11-15.
    Report Number: DIT-02-049
    Repository staff approval on: 21 Jan 2003

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