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- W63236435 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 $mathsf{APX}$-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 $L$." @default.
- W63236435 created "2016-06-24" @default.
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- W63236435 date "2007-01-01" @default.
- W63236435 modified "2023-09-23" @default.
- W63236435 title "On Approximating Restricted Cycle Covers." @default.
- W63236435 hasPublicationYear "2007" @default.
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