Approximation Algorithms for Restricted Cycle Covers Based on Cycle Decompositions

Details Approximation Algorithms for Restricted Cycle Covers Based on Cycle Decompositions Approximation Algorithms for Restricted Cycle Covers Based on Cycle Decompositions

2006-04-06

arxiv.org/abs/cs/0604020v4

Computer Science

Data Structures and Algorithms

This paper has been joint with "On Approximating Restricted Cycle Covers" (cs.CC/0504038). Please refer to that paper. The pap

Scientific paper

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. The weight of a cycle cover of an edge-weighted graph is the sum of the weights of its edges. We come close to settling the complexity and approximability of computing L-cycle covers. On the one hand, we show that for almost all L, computing L-cycle covers of maximum weight in directed and undirected graphs is APX-hard and NP-hard. Most of our hardness results hold even if the edge weights are restricted to zero and one. On the other hand, we show that the problem of computing L-cycle covers of maximum weight can be approximated within a factor of 2 for undirected graphs and within a factor of 8/3 in the case of directed graphs. This holds for arbitrary sets L.

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