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Parameterized Query Complexity of Hitting Set Using Stability of Sunflowers

Authors Arijit Bishnu, Arijit Ghosh, Sudeshna Kolay, Gopinath Mishra, Saket Saurabh

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ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Query complexity
  • Hitting set
  • Parameterized complexity

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Abstract

In this paper, we study the query complexity of parameterized decision and optimization versions of Hitting-Set. We also investigate the query complexity of Packing. In doing so, we use generalizations to hypergraphs of an earlier query model, known as BIS introduced by Beame et al. in ITCS'18. The query models considered are the GPIS and GPISE oracles. The GPIS and GPISE oracles are used for the decision and optimization versions of the problems, respectively. We use color coding and queries to the oracles to generate subsamples from the hypergraph, that retain some structural properties of the original hypergraph. We use the stability of the sunflowers in a non-trivial way to do so.

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Arijit Bishnu, Arijit Ghosh, Sudeshna Kolay, Gopinath Mishra, and Saket Saurabh. Parameterized Query Complexity of Hitting Set Using Stability of Sunflowers. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 25:1-25:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ISAAC.2018.25

Author Details

Arijit Bishnu
  • Indian Statistical Institute, Kolkata, India
Arijit Ghosh
  • The Institute of Mathematical Sciences, Chennai, India
Sudeshna Kolay
  • Eindhoven University of Technology, Eindhoven, Netherlands
Gopinath Mishra
  • Indian Statistical Institute, Kolkata, India
Saket Saurabh
  • The Institute of Mathematical Sciences, Chennai, India

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