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Multiple hypernode hitting sets and smallest two-cores with targets

Peter Damaschke (Institutionen för data- och informationsteknik, Datavetenskap, Algoritmer (Chalmers) ; Institutionen för data- och informationsteknik, Datavetenskap, Bioinformatik (Chalmers))
Journal of Combinatorial Optimization (special issue COCOA 2008) (1382-6905). Vol. 18 (2009), 3, p. 294-306.
[Artikel, refereegranskad vetenskaplig]

The multiple weighted hitting set problem is to find a subset of nodes in a hypergraph that hits every hyperedge in at least m nodes. We extend the problem to a notion of hypergraphs with so-called hypernodes and show that, for m=2, it remains fixed-parameter tractable (FPT), parameterized by the number of hyperedges. This is accomplished by a nontrivial extension of the dynamic programming algorithm for hypergraphs. The algorithm might be interesting for certain assignment problems, but here we need it as a tool to solve another problem motivated by network analysis: A d-core of a graph is a subgraph in which every vertex has at least d neighbors. We give an FPT algorithm that computes a smallest 2-core including a given set of target vertices, where the number of targets is the parameter. This FPT result is best possible in the sense that no FPT algorithm for 3-cores can be expected.

Nyckelord: hitting set, job assignment, parameterized algorithm, dynamic programming on subsets, cores in graphs



Denna post skapades 2009-11-10. Senast ändrad 2015-02-11.
CPL Pubid: 101452