Approximation Algorithms for Restricted Cycle Covers Based on Cycle Decompositions

  • Bodo Manthey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4271)

Abstract

A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L ⊆ ℕ. For most sets L, the problem of computing L-cycle covers of maximum weight is NP-hard and APX-hard.

We devise polynomial-time approximation algorithms for L-cycle covers. More precisely, we present a factor 2 approximation algorithm for computing L-cycle covers of maximum weight in undirected graphs and a factor 20/7 approximation algorithm for the same problem in directed graphs. Both algorithms work for arbitrary sets L. To do this, we develop a general decomposition technique for cycle covers.

Finally, we show tight lower bounds for the approximation ratios achievable by algorithms based on such decomposition techniques.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bodo Manthey
    • 1
  1. 1.InformatikUniversität des SaarlandesSaarbrückenGermany

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