Beyersdorff, O, Galesi, N and Lauria, M (2011) Parameterized complexity of DPLL search procedures. In: Sakallah, KA and Simon, L, (eds.) Theory and Applications of Satisfiability Testing - SAT 2011. SAT 2011, 19 - 22 June 2011, Ann Arbor, MI, USA. Springer Verlag , 5 - 18 . ISBN 978-3-642-21580-3
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 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  of understanding the Resolution complexity of this family of formulas.
|Copyright, Publisher and Additional Information:||© 2011, Springer Verlag. This is an author produced version of a paper published in Theory and Applications of Satisfiability Testing - SAT 2011. Uploaded in accordance with the publisher's self-archiving policy. The original publication is available at www.springerlink.com|
|Institution:||The University of Leeds|
|Academic Units:||The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds)|
|Depositing User:||Symplectic Publications|
|Date Deposited:||03 Dec 2012 10:37|
|Last Modified:||25 Oct 2016 10:05|