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Parameterized Complexity and Kernelizability of Max Ones and Exact Ones Problems

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Published:03 February 2016Publication History
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Abstract

For a finite set Γ of Boolean relations, Max Ones SAT(Γ) and Exact Ones SAT(Γ) are generalized satisfiability problems where every constraint relation is from Γ, and the task is to find a satisfying assignment with at least/exactly k variables set to 1, respectively. We study the parameterized complexity of these problems, including the question whether they admit polynomial kernels. For Max Ones SAT(Γ), we give a classification into five different complexity levels: polynomial-time solvable, admits a polynomial kernel, fixed-parameter tractable, solvable in polynomial time for fixed k, and NP-hard already for k = 1. For Exact Ones SAT(Γ), we refine the classification obtained earlier by taking a closer look at the fixed-parameter tractable cases and classifying the sets Γ for which Exact Ones SAT(Γ) admits a polynomial kernel.

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  1. Parameterized Complexity and Kernelizability of Max Ones and Exact Ones Problems

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    • Published in

      cover image ACM Transactions on Computation Theory
      ACM Transactions on Computation Theory  Volume 8, Issue 1
      February 2016
      97 pages
      ISSN:1942-3454
      EISSN:1942-3462
      DOI:10.1145/2889309
      Issue’s Table of Contents

      Copyright © 2016 ACM

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 3 February 2016
      • Accepted: 1 September 2015
      • Revised: 1 July 2015
      • Received: 1 May 2014
      Published in toct Volume 8, Issue 1

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