Approximation algorithms for cycle packing problems

Michael Krivelevich*, Zeev Nutov, Raphael Yuster

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

17 Scopus citations


The cycle packing number vc(G) of a graph G is the maximum number of pairwise edge-disjoint cycles in G. Computing vc(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(n2/3)-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 languageEnglish
Number of pages6
StatePublished - 2005
EventSixteenth Annual ACM-SIAM Symposium on Discrete Algorithms - Vancouver, BC, United States
Duration: 23 Jan 200525 Jan 2005


ConferenceSixteenth Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CityVancouver, BC


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