Approximation Algorithms for Restricted Cycle Covers Based on Cycle Decompositions
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.
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