Sorting Permutations by Reversals and Eulerian Cycle Decompositions
SIAM Journal on Discrete Mathematics
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Genome Rearrangements and Sorting by Reversals
SIAM Journal on Computing
Approximation algorithms for cycle packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms and hardness results for cycle packing problems
ACM Transactions on Algorithms (TALG)
CTL Model-Checking with Graded Quantifiers
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Efficient approximation algorithms for shortest cycles in undirected graphs
Information Processing Letters
Induced Packing of Odd Cycles in a Planar Graph
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Fundamenta Informaticae - Advances in Computational Logic (CIL C08)
Approximability of packing disjoint cycles
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Efficient approximation algorithms for shortest cycles in undirected graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Approximation algorithms for grooming in optical network design
Theoretical Computer Science
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Information Processing Letters
Induced packing of odd cycles in planar graphs
Theoretical Computer Science
Disjoint cycles: integrality gap, hardness, and approximation
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Exact and approximation algorithms for DNA tag set design
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
An efficient algorithm for finding maximum cycle packings in reducible flow graphs
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Disjoint cycles intersecting a set of vertices
Journal of Combinatorial Theory Series B
Fundamenta Informaticae - Advances in Computational Logic (CIL C08)
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Given an undirected graph G with n nodes and m edges, we address the problem of finding a largest collection of edge-disjoint cycles in G. The problem, dubbed CYCLE PACKING, is very closely related to a few genome rearrangement problems in computational biology. In this paper, we study the complexity and approximability of CYCLE PACKING, about which very little is known although the problem is natural and has practical applications. We show that the problem is APX- hard but can be approximated within a factor of O(logn) by a simple greedy approach. We do not know whether the O(log n) factor is tight, but we give a nontrivial example for which the ratio achieved by greedy is not constant, namely Ω(√logn/(loglogn)). We also show that, for "not too sparse" graphs, i.e., graphs for which m = Ω (n1+1/t+δ) for some positive integer t and for any fixed δ 0, we can achieve an approximation arbitrarily close to 2t/3 in polynomial time. In particular, for any ε 0, this yields a 4/3 + ε approximation when m = Ω(n3/2+δ), therefore also for dense graphs. Finally, we briefly discuss a natural linear programming relaxation for the problem.