Kernelizations for Parameterized Counting Problems

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. In the last decade, parameterized complexity matured as a field of refined complexity analyses of algorithms and decision problems. It replaces the classical notion of tractability with fixed parameter tractability [12], requiring tractable problems to be solvable by a deterministic algorithm in time f...

• Type: Conference
• Year: 2007
• Where: TAMC
• Authors: Marc Thurley
• Keywords: Counting Problems, Parameter, Parameter Algorithm, TAMC 2007