Parameterized Complexity of DPLL Search Procedures

  • Olaf Beyersdorff
  • Nicola Galesi
  • Massimo Lauria
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6695)


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.


Random Graph Proof System Conjunctive Normal Form Parameterized Resolution Satisfying Assignment 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Olaf Beyersdorff
    • 1
  • Nicola Galesi
    • 2
  • Massimo Lauria
    • 2
  1. 1.Institut für Theoretische InformatikLeibniz Universität HannoverGermany
  2. 2.Dipartimento di InformaticaSapienza Università di RomaItaly

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