Approximation Algorithms for Restricted Cycle Covers Based on Cycle Decompositions
Abstract
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.
Cite
@article{arxiv.cs/0604020,
title = {Approximation Algorithms for Restricted Cycle Covers Based on Cycle Decompositions},
author = {Bodo Manthey},
journal= {arXiv preprint arXiv:cs/0604020},
year = {2007}
}
Comments
This paper has been joint with "On Approximating Restricted Cycle Covers" (cs.CC/0504038). Please refer to that paper. The paper "Approximation Algorithms for Restricted Cycle Covers Based on Cycle Decompositions" is now obsolete