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- W4367060897 abstract "This paper deals with the problem of finding a collection of vertex-disjoint paths in a given graph G=(V,E) such that each path has at least four vertices and the total number of vertices in these paths is maximized. The problem is NP-hard and admits an approximation algorithm which achieves a ratio of 2 and runs in O(|V|^8) time. The known algorithm is based on time-consuming local search, and its authors ask whether one can design a better approximation algorithm by a completely different approach. In this paper, we answer their question in the affirmative by presenting a new approximation algorithm for the problem. Our algorithm achieves a ratio of 1.874 and runs in O(min{|E|^2|V|^2, |V|^5}) time. Unlike the previously best algorithm, ours starts with a maximum matching M of G and then tries to transform M into a solution by utilizing a maximum-weight path-cycle cover in a suitably constructed graph." @default.
- W4367060897 created "2023-04-27" @default.
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- W4367060897 date "2023-04-25" @default.
- W4367060897 modified "2023-10-01" @default.
- W4367060897 title "An Approximation Algorithm for Covering Vertices by 4^+-Paths" @default.
- W4367060897 doi "https://doi.org/10.48550/arxiv.2304.12779" @default.
- W4367060897 hasPublicationYear "2023" @default.
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