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The Union of Minimal Hitting Sets: Parameterized Combinatorial Bounds and Counting

  • Peter Damaschke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)

Abstract

We study how many vertices in a rank-r hypergraph can belong to the union of all inclusion-minimal hitting sets of at most k vertices. This union is interesting in certain combinatorial inference problems with hitting sets as hypotheses, as it provides a problem kernel for likelihood computations (which are essentially counting problems) and contains the most likely elements of hypotheses. We give worst-case bounds on the size of the union, depending on parameters r,k and the size k * of a minimum hitting set. (Note that k ≥ k * is allowed.) Our result for r = 2 is tight. The exact worst-case size for any r ≥ 3 remains widely open. By several hypergraph decompositions we achieve nontrivial bounds with potential for further improvements.

Keywords

algorithms parameterization combinatorial inference counting hypergraph transversals 

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Peter Damaschke
    • 1
  1. 1.School of Computer Science and Engineering, Chalmers University, 41296 GöteborgSweden

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