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

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

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

Vol. 18 294-306Computer Science

10.1007/s10878-009-9234-9