Graph decomposition is NPC - a complete proof of Holyer's conjecture
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Journal of Computer and System Sciences
Packing Digraphs with Directed Closed Trails
Combinatorics, Probability and Computing
Graph decomposition and a greedy algorithm for edge-disjoint paths
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Packing cycles in undirected graphs
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Hardness of the undirected edge-disjoint paths problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Approximation algorithms for cycle packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Asymmetric k-center is log* n-hard to approximate
Journal of the ACM (JACM)
Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms and hardness results for cycle packing problems
ACM Transactions on Algorithms (TALG)
Combinatorica
Disjoint cycles: integrality gap, hardness, and approximation
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Induced Packing of Odd Cycles in a Planar Graph
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Approximation algorithms for grooming in optical network design
Theoretical Computer Science
Induced packing of odd cycles in planar graphs
Theoretical Computer Science
Disjoint cycles intersecting a set of vertices
Journal of Combinatorial Theory Series B
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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(√log n) [14,15]. 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 [1,9], we show that the undirected edge-disjoint cycle packing problem has an integrality gap of Ω(√log n/log log n) and furthermore it is quasi-NP-hard to approximate the edge-disjoint cycle problem within ratio of O(log1/2-Ɛ n) for any constant Ɛ 0. The same results hold for the problem of packing vertex-disjoint cycles.