Multiple hypernode hitting sets and smallest two-cores with targets
Journal article, 2009

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.

parameterized algorithm

job assignment

hitting set

dynamic programming on subsets

cores in graphs

Author

Peter Damaschke

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Journal of Combinatorial Optimization

1382-6905 (ISSN) 1573-2886 (eISSN)

Vol. 18 294-306

Subject Categories

Computer Science

DOI

10.1007/s10878-009-9234-9