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Parameterized Complexity of DPLL Search Procedures

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Theory and Applications of Satisfiability Testing - SAT 2011 (SAT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6695))

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Abstract

We study the performance of DPLL algorithms on parameterized problems. In particular, we investigate how difficult it is to decide whether small solutions exist for satisfiability and other combinatorial problems. For this purpose we develop a Prover-Delayer game which models the running time of DPLL procedures and we establish an information-theoretic method to obtain lower bounds to the running time of parameterized DPLL procedures. We illustrate this technique by showing lower bounds to the parameterized pigeonhole principle and to the ordering principle. As our main application we study the DPLL procedure for the problem of deciding whether a graph has a small clique. We show that proving the absence of a k-clique requires n Ω(k) steps for a non-trivial distribution of graphs close to the critical threshold. For the restricted case of tree-like Parameterized Resolution, this result answers a question asked in [11] of understanding the Resolution complexity of this family of formulas.

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Author information

Authors and Affiliations

  1. Institut für Theoretische Informatik, Leibniz Universität Hannover, Germany

    Olaf Beyersdorff

  2. Dipartimento di Informatica, Sapienza Università di Roma, Italy

    Nicola Galesi & Massimo Lauria

Authors
  1. Olaf Beyersdorff
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  2. Nicola Galesi
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  3. Massimo Lauria
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Editor information

Editors and Affiliations

  1. University of Michigan, 48109, Ann Arbor, MI, USA

    Karem A. Sakallah

  2. LRI / CNRS UMR8623 / INRIA Saclay, Univ Paris-Sud, F-91405, Orsay, France

    Laurent Simon

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Beyersdorff, O., Galesi, N., Lauria, M. (2011). Parameterized Complexity of DPLL Search Procedures. In: Sakallah, K.A., Simon, L. (eds) Theory and Applications of Satisfiability Testing - SAT 2011. SAT 2011. Lecture Notes in Computer Science, vol 6695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21581-0_3

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  • DOI: https://doi.org/10.1007/978-3-642-21581-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21580-3

  • Online ISBN: 978-3-642-21581-0

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