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. 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.
Original language | English |
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Pages (from-to) | 181-206 |
Number of pages | 26 |
Journal | SIAM journal on computing |
Volume | 38 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2008 |