Exact algorithms and applications for Tree-like Weighted Set Cover (2006)
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| Venue: | JOURNAL OF DISCRETE ALGORITHMS |
| Citations: | 6 - 4 self |
BibTeX
@TECHREPORT{Guo06exactalgorithms,
author = {Jiong Guo and Rolf Niedermeier},
title = {Exact algorithms and applications for Tree-like Weighted Set Cover},
institution = {JOURNAL OF DISCRETE ALGORITHMS},
year = {2006}
}
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Abstract
We introduce an NP-complete special case of the Weighted Set Cover problem and show its fixed-parameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given collection C of subsets of a some base set S should be “tree-like.” That is, the subsets in C can be organized in a tree T such that every subset one-to-one corresponds to a tree node and, for each element s of S, the nodes corresponding to the subsets containing s induce a subtree of T. This is equivalent to the problem of finding a minimum edge cover in an edge-weighted acyclic hypergraph. Our main result is an algorithm running in O(3 k ·mn) time where k denotes the maximum subset size, n: = |S|, and m: = |C|. The algorithm also implies a fixed-parameter tractability result for the NP-complete Multicut in Trees problem, complementing previous approximation results. Our results find applications in computational biology in phylogenomics and for saving memory in tree decomposition based graph algorithms.







