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Towards Optimal and Expressive Kernelization for d-Hitting Set

  • René van Bevern
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7434)

Abstract

A sunflower in a hypergraph is a set of hyperedges pairwise intersecting in exactly the same vertex set. Sunflowers are a useful tool in polynomial-time data reduction for problems formalizable as d-Hitting Set, the problem of covering all hyperedges (of cardinality at most d) of a hypergraph by at most k vertices. Additionally, in fault diagnosis, sunflowers yield concise explanations for “highly defective structures”. We provide a linear-time algorithm that, by finding sunflowers, transforms an instance of d-Hitting Set into an equivalent instance comprising at most O(k d ) hyperedges and vertices. In terms of parameterized complexity, we show a problem kernel with asymptotically optimal size (unless coNP ⊆ NP/poly). We show that the number of vertices can be reduced to O(k d − 1) with additional processing in O(k 1.5d ) time—nontrivially combining the sunflower technique with problem kernels due to Abu-Khzam and Moser.

Keywords

Fault Diagnosis Character String Boolean Circuit Concise Explanation Problem Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • René van Bevern
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany

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