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)
\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
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Approximations for ATSP with Parametrized Triangle Inequality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Computing Cycle Covers without Short Cycles
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
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
An approximation algorithm for maximum triangle packing
Discrete Applied Mathematics
Improved deterministic approximation algorithms for Max TSP
Information Processing Letters
Improved approximation algorithms for metric max TSP
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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
Minimum-weight cycle covers and their approximability
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
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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. For most sets L, the problem of computing L-cycle covers of maximum weight is NP-hard and APX-hard. We devise polynomial-time approximation algorithms for L-cycle covers. More precisely, we present a factor 2 approximation algorithm for computing L-cycle covers of maximum weight in undirected graphs and a factor 20/7 approximation algorithm for the same problem in directed graphs. Both algorithms work for arbitrary sets L. To do this, we develop a general decomposition technique for cycle covers. Finally, we show tight lower bounds for the approximation ratios achievable by algorithms based on such decomposition techniques.