Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Handbook of combinatorics (vol. 1)
Handbook of combinatorics (vol. 1)
Some APX-completeness results for cubic graphs
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Square-Free 2-Factor Problem in Bipartite Graphs
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Computing Cycle Covers without Short Cycles
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
A new approximation algorithm for the asymmetric TSP with triangle inequality
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs
Journal of the ACM (JACM)
Terminal backup, 3D matching, and covering cubic graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Terminal Backup, 3D Matching, and Covering Cubic Graphs
SIAM Journal on Computing
Improved approximation algorithms for metric maximum ATSP and maximum 3-cycle cover problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Improved approximation algorithms for metric maximum ATSP and maximum 3-cycle cover problems
Operations Research Letters
35/44-Approximation for asymmetric maximum TSP with triangle inequality
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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A cycle cover of a directed graph is a collection of node disjoint cycles such that every node is part of exactly one cycle. A k-cycle cover is a cycle cover in which every cycle has length at least k. While deciding whether a directed graph has a 2-cycle cover is solvable in polynomial time, deciding whether it has a 3-cycle cover is already NP-complete. Given a directed graph with nonnegative edge weights, a maximum weight 2-cycle cover can be computed in polynomial time, too. We call the corresponding optimization problem of finding a maximum weight 3-cycle cover Max-3-DCC.In this paper we present two polynomial time approximation algorithms for Max-3-DCC. The heavier of the 3-cycle covers computed by these algorithms has at least a fraction of 3/5- 驴, for any 驴 0, of the weight of a maximum weight 3-cycle cover.As a lower bound, we prove that Max-3-DCC is APX-complete, even if the weights fulfil the triangle inequality.