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International Conference on Principles and Practice of Constraint Programming

CP 2001: Principles and Practice of Constraint Programming — CP 2001 pp 121–136Cite as

Random 3-SAT and BDDs: The Plot Thickens Further

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2239))

Abstract

This paper contains an experimental study of the impact of the construction strategy of reduced, ordered binary decision diagrams (ROBDDs) on the average-case computational complexity of random 3-SAT, using the CUDD package.We study the variation of median running times for a large collection of random 3-SAT problems as a function of the density as well as the order (number of variables) of the instances.We used ROBDD-based pure SAT-solving algorithms, which we obtained by an aggressive application of existential quantification, augmented by several heuristic optimizations. Our main finding is that our algorithms display an “easy-hard-less-hard” pattern that is quite similar to that observed earlier for search-based solvers. When we start with low-density instances and then increase the density, we go from a region of polynomial running time, to a region of exponential running time, where the exponent first increases and then decreases as a function of the density. The locations of both transitions, from polynomial to exponential and from increasing to decreasing exponent, are algorithm dependent. In particular, the running time peak is quite independent from the crossover density of 4.26 (where the probability of satisfiability declines precipitously); it occurs at density 3.8 for one algorithm and at density 2.3 for for another, demonstrating that the correlation between the crossover density and computational hardness is algorithm dependent.

Part of this work was done while this author was on sabbatical at Rice University, funded in part by CONACyT grant 145502.

Work partially supported by NSF grants IIS-9908435, IIS-9978135, CCR-9988322, and EIA- 0086264, and by a grant from the Intel Corporation.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Instituto Tecnologico Autonomo de Mexico, Rio Hondo 1, 01000, Mexico City, Mexico

    Alfonso San Miguel Aguirre

  2. Department of Computer Science, Rice University, 6100 S. Main St MS 132, 77005-1892, Houston, TX, USA

    MosheY. Vardi

Authors
  1. Alfonso San Miguel Aguirre
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  2. MosheY. Vardi
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Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of York, YO10 5DD, Heslington, York, UK

    Toby Walsh

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© 2001 Springer-Verlag Berlin Heidelberg

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Aguirre, A.S.M., Vardi, M. (2001). Random 3-SAT and BDDs: The Plot Thickens Further. In: Walsh, T. (eds) Principles and Practice of Constraint Programming — CP 2001. CP 2001. Lecture Notes in Computer Science, vol 2239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45578-7_9

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  • DOI: https://doi.org/10.1007/3-540-45578-7_9

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  • Print ISBN: 978-3-540-42863-3

  • Online ISBN: 978-3-540-45578-3

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