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  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.
|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||Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms|
|Period||23/01/05 → 25/01/05|