## Abstract

The cycle packing number v_{c}(G) of a graph G is the maximum number of pairwise edge-disjoint cycles in G. Computing v_{c}(G) is an NP-hard problem. We present approximation algorithms for computing v _{c}(G) in both the undirected and directed cases. In the undirected case we analyze the modified greedy algorithm suggested in [4] and show that it has approximation ratio O(√log n) where n = |V(G)|, and this is tight. This improves upon the previous O(log n) upper bound for the approximation ratio of this algorithm. In the directed case we present a √n-approximation algorithm. Finally, we give an O(n^{2/3})-approximation algorithm for the problem of rinding a maximum number of edge-disjoint cycles that intersect a specified subset S of vertices. Our approximation ratios are the currently best known ones and, in addition, provide bounds on the integrality gap of standard LP-relaxations to these problems.

Original language | English |
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Pages | 556-561 |

Number of pages | 6 |

State | Published - 2005 |

Event | Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms - Vancouver, BC, United States Duration: 23 Jan 2005 → 25 Jan 2005 |

### Conference

Conference | Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms |
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Country/Territory | United States |

City | Vancouver, BC |

Period | 23/01/05 → 25/01/05 |