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Approximability of Packing Disjoint Cycles

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Abstract

Given a graph G, the edge-disjoint cycle packing problem is to find the largest set of cycles of which no two share an edge. For undirected graphs, the best known approximation algorithm has ratio \(O(\sqrt{\log n})\) (Krivelevich et al. in ACM Trans. Algorithms, 2009, to appear). In fact, they proved the same upper bound for the integrality gap of this problem by presenting a simple greedy algorithm. Here we show that this is almost best possible. By modifying integrality gap and hardness results for the edge-disjoint paths problem (Andrews et al. in Proc. of 46th IEEE FOCS, pp. 226–244, 2005; Chuzhoy and Khanna in New hardness results for undirected edge disjoint paths. Manuscript, 2005), we show that the undirected edge-disjoint cycle packing problem is quasi-NP-hard to approximate within ratio of \(O(\log^{\frac{1}{2}-\epsilon}n)\) for any constant ε>0. The same result holds for the problem of packing vertex-disjoint cycles.

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Authors and Affiliations

  1. Department of Computing Science, University of Alberta, Edmonton, Alberta, T6G 2E8, Canada

    Zachary Friggstad & Mohammad R. Salavatipour

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  1. Zachary Friggstad
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  2. Mohammad R. Salavatipour
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Correspondence to Mohammad R. Salavatipour.

Additional information

A preliminary version appeared [9] in Proceedings of ISAAC 2007.

The first author was supported by NSERC and iCore scholarships and the 2nd author was supported by NSERC and an Alberta Ingenuity New Faculty award.

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Friggstad, Z., Salavatipour, M.R. Approximability of Packing Disjoint Cycles. Algorithmica 60, 395–400 (2011). https://doi.org/10.1007/s00453-009-9349-5

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  • DOI: https://doi.org/10.1007/s00453-009-9349-5

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