SIAM Journal on Discrete Mathematics
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Linear approximation of shortest superstrings
Journal of the ACM (JACM)
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
\boldmath A $2\frac12$-Approximation Algorithm for Shortest Superstring
SIAM Journal on Computing
Approximation algorithms for the TSP with sharpened triangle inequality
Information Processing Letters
Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs
Journal of the ACM (JACM)
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
An improved approximation algorithm for the asymmetric TSP with strengthened triangle inequality
Journal of Discrete Algorithms
On the relationship between ATSP and the cycle cover problem
Theoretical Computer Science
An approximation algorithm for maximum triangle packing
Discrete Applied Mathematics
Improved deterministic approximation algorithms for Max TSP
Information Processing Letters
Approximation algorithms for restricted cycle covers based on cycle decompositions
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
On approximating restricted cycle covers
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
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
On the complexity of the k-customer vehicle routing problem
Operations Research Letters
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A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L⊆N. We investigate how well L-cycle covers of minimum weight can be approximated. For undirected graphs, we devise a polynomial-time approximation algorithm that achieves a constant approximation ratio for all sets L. On the other hand, we prove that the problem cannot be approximated within a factor of 2 - Ɛ for certain sets L. For directed graphs, we present a polynomial-time approximation algorithm that achieves an approximation ratio of O(n), where n is the number of vertices. This is asymptotically optimal: We show that the problem cannot be approximated within a factor of o(n). To contrast the results for cycle covers of minimum weight, we show that the problem of computing L-cycle covers of maximum weight can, at least in principle, be approximated arbitrarily well.