Minimum-Weight Cycle Covers and Their Approximability

  • Bodo Manthey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4769)


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.

We investigate how well L-cycle covers of minimum weight can be approximated. For undirected graphs, we devise a polynomial-time approximation algorithm that achieves a constant approximation ratio for all sets L. On the other hand, we prove that the problem cannot be approximated within a factor of 2 − ε for certain sets L.

For directed graphs, we present a polynomial-time approximation algorithm that achieves an approximation ratio of O(n), where n is the number of vertices. This is asymptotically optimal: We show that the problem cannot be approximated within a factor of o(n).

To contrast the results for cycle covers of minimum weight, we show that the problem of computing L-cycle covers of maximum weight can, at least in principle, be approximated arbitrarily well.


Approximation Algorithm Undirected Graph Approximation Ratio Edge Weight Minimum Weight 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Bodo Manthey
    • 1
  1. 1.Yale University, Department of Computer Science, P.O. Box 208285, New Haven, CT 06520-8285USA

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