Chordless paths through three vertices
Theoretical Computer Science - Parameterized and exact computation
Parameterized complexity of the smallest degree-constrained subgraph problem
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Some fixed-parameter tractable classes of hypergraph duality and related problems
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Parameterized algorithms for HITTING SET: the weighted case
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
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The multiple weighted hitting set problem is to find a subset of nodes in a hypergraph that hits every hyperedge in at least mnodes. We extend the problem to a notion of hypergraphs with so-called hypernodes and show that it remains fixed-parameter tractable (FPT) for m= 2, with the number of hyperedges as the parameter. This is accomplished by a nontrivial extension of the known dynamic programming algorithm for usual hypergraphs. The result might be of independent interest for assignment problems, but here we need it as an auxiliary result to solve a different problem motivated by network analysis: We give an FPT algorithm that computes a smallest 2-core including a given set of target vertices in a graph, with the number of targets as the parameter. (A d-core is a subgraph where every vertex has degree at least dwithin the subgraph.) This FPT result is best possible, in the sense that an FPT algorithm for 3-cores cannot exist, for simple reasons.