Multiple hypernode hitting sets and smallest two-cores with targets

Peter Damaschke ()
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Peter Damaschke: Chalmers University

Journal of Combinatorial Optimization, 2009, vol. 18, issue 3, No 5, 294-306

Abstract: Abstract 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.

Keywords: Hitting set; Job assignment; Parameterized algorithms; Dynamic programming on subsets; Cores in graphs (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-009-9234-9

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