Kernelizations for parameterized counting problems

Authors:
Marc Thurley
Affiliations:
Institut für Informatik, Humboldt-Universität zu Berlin
Venue:
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Year:
2007

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Abstract

Kernelizations are an important tool in designing fixed parameter algorithms for parameterized decision problems. We introduce an analogous notion for counting problems, to wit, counting kernelizations which turn out to be equivalent to the fixed parameter tractability of counting problems. Furthermore, we study the application of well-known kernelization techniques to counting problems. Among these are the Buss Kernelization and the Crown Rule Reduction for the vertex cover problem. Furthermore, we show how to adapt kernelizations for the hitting set problem on hypergraphs with hyperedges of bounded cardinality and the unique hitting set problem to their counting analogs.