Beyersdorff, O, Galesi, N and Lauria, M (2013) Parameterized complexity of DPLL search procedures. ACM Transactions on Computational Logic, 14 (3). 20. ISSN 1529-3785
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 that 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 nontrivial distribution of graphs close to the critical threshold. For the restricted case of tree-like Parameterized Resolution, this result answers a question asked by Beyersdorff et al. [2012] of understanding the Resolution complexity of this family of formulas.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © ACM, 2013. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Computational Logic, 14, 3, 20, 2013, http://doi.acm.org/10.1145/2499937.2499941 |
Keywords: | Algorithms; complexity; parameterized complexity; proof; prover-delayer games; resolution; theory |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 Jun 2014 10:20 |
Last Modified: | 21 Jan 2018 03:07 |
Published Version: | http://dx.doi.org/10.1145/2499937.2499941 |
Status: | Published |
Publisher: | Association for Computing Machinery |
Identification Number: | 10.1145/2499937.2499941 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:79311 |