Pseudo-Kernelization: A Branch-then-Reduce Approach for FPT Problems

Abstract

Pseudo-kernelization is introduced in this paper as a new strategy for improving fixed-parameter algorithms. This new technique works for bounded search tree algorithms by identifying favorable branching conditions whose absence could be used to reduce the size of corresponding problem instances. Pseudo-kernelization applies well to hitting set problems. It can be used either to improve the search tree size of a 3-Hitting-Set algorithm from O*(2.179k) to O*(2.05k), or to improve the kernel size from k3 to 27k. In this paper the parameterized 3-Hitting-Set and Face Cover problems are used as typical examples.

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Correspondence to Faisal N. Abu-Khzam.

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Abu-Khzam, F. Pseudo-Kernelization: A Branch-then-Reduce Approach for FPT Problems. Theory Comput Syst 41, 399–410 (2007). https://doi.org/10.1007/s00224-007-1344-0

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Keywords

  • Search Tree
  • Vertex Cover
  • Kernel Size
  • Reduction Rule
  • Double Edge