Abstract
This paper introduces a notational frame to characterize the four basic product-based Message Passing (MP) heuristics currently available for SAT: Belief Propagation (BP), Survey Propagation (SP), Expectation Maximization BP Global (EMBPG) and Expectation Maximization SP Global (EMSPG). Using this framework, the paper introduces indirect structural interpolation (ISI). Using this technique, we create a hierarchy of heuristics – each new level in this hierarchy consists of heuristics strictly more general than their predecessors. The final result is the ρσPMPi heuristic, which is able to mimic all product-based MP heuristics and is hence a generalization for all them.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aurell, E., Gordon, U., Kirkpatrick, S.: Comparing Beliefs, Surveys and Random Walks. In: Adv. in Neural Information Processing Sys. 17, p. 49. MIT Press (2005)
Battaglia, D., Kolář, M., Zecchina, R.: Minimizing energy below the glass thresholds. Physical Review E 70, 036107 (2004)
Biere, A.: Lingeling SAT solver, Version ala-b02aala, http://fmv.jku.at/lingeling/lingeling-ala-b02aa1a-121013.tar.gz
Braunstein, A., Mézard, M., Zecchina, R.: Survey Propagation: An Algorithm for Satisfiability. Journal of Rand. Struct. and Algo., 201 (2005)
Chavas, J., Furtlehner, C., Mézard, M., Zecchina, R.: Survey-propagation decimation through distributed local computations. Journal of Statistical Mechanics: Theory and Experiment (2005) 1742-5468 / 05 / P11016
Gableske, O.: Dimetheus SAT solver, Version 1.6, https://www.gableske.net/dimetheus
Gableske, O., Müelich, S., Diepold, D.: On the Performance of CDCL based Message Passing Inspired Decimation using ρσPMPi. Submitted to the Proceedings of the Pragmatics of SAT Workshop, POS 2013 (2013)
Hsu, E.I., McIlraith, S.A.: VARSAT: Integrating Novel Probabilistic Inference Techniques with DPLL Search. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 377–390. Springer, Heidelberg (2009)
Hsu, E.I., McIlraith, S.A.: Characterizing Propagation Methods for Boolean Satisfiability. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 325–338. Springer, Heidelberg (2006)
Hsu, E.I., Muise, C.J., Beck, J.C., McIlraith, S.A.: Probabilistically Estimating Backbones and Variable Bias: Experimental Overview. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 613–617. Springer, Heidelberg (2008)
Hsu, E., Kitching, M., Bacchus, F., McIlraith, S.: Using Expectation Maximization to Find Likely Assignments for Solving CSPs. In: AAAI 2007, p. 224. AAAI Press (2007)
Jeroslow, R., Wang, J.: Solving Propositional Satisfiability Problems. Annals of Mathematics and Artificial Intelligence 1, 167 (1990)
Schischang, K., Frey, B., Loeliger, H.: Factor Graphs and the sum-product algorithm. IEEE Trans. Inform. Theory 47, 498 (2002)
Maneva, E., Mossel, E., Wainwright, M.J.: A New Look at Survey Propagation and its Generalizations, arXiv:cs/0409012v3, 01 (February 2008)
Mézard, M., Parisi, G.: The cavity method at zero temperature. Journal of Statistical Physics 111(1/2) (April 2003)
Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: DAC 2001, p. 530. ACM (2001)
Pipatsrisawat, K., Darwiche, A.: A lightweight component caching scheme for Satisfiability Solvers. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 294–299. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gableske, O. (2013). On the Interpolation between Product-Based Message Passing Heuristics for SAT. In: Järvisalo, M., Van Gelder, A. (eds) Theory and Applications of Satisfiability Testing – SAT 2013. SAT 2013. Lecture Notes in Computer Science, vol 7962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39071-5_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-39071-5_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39070-8
Online ISBN: 978-3-642-39071-5
eBook Packages: Computer ScienceComputer Science (R0)