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Multiple hypernode hitting sets and smallest two-cores with targets

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  • Peter Damaschke

    (Chalmers University)

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.

Suggested Citation

  • Peter Damaschke, 2009. "Multiple hypernode hitting sets and smallest two-cores with targets," Journal of Combinatorial Optimization, Springer, vol. 18(3), pages 294-306, October.
    • Handle: RePEc:spr:jcomop:v:18:y:2009:i:3:d:10.1007_s10878-009-9234-9
    DOI: 10.1007/s10878-009-9234-9
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    Cited by:

    1. Peter Damaschke, 2015. "Parameterizations of hitting set of bundles and inverse scope," Journal of Combinatorial Optimization, Springer, vol. 29(4), pages 847-858, May.

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