Abstract
Unsatisfiability-based algorithms for Maximum Satisfiability (MaxSAT) have been shown to be very effective in solving several classes of problem instances. These algorithms rely on successive calls to a SAT solver, where an unsatisfiable subformula is identified at each iteration. However, in some cases, the SAT solver returns unnecessarily large subformulas. In this paper a new technique is proposed to partition the MaxSAT formula in order to identify smaller unsatisfiable subformulas at each call of the SAT solver. Preliminary experimental results analyze the effect of partitioning the MaxSAT formula into communities. This technique is shown to significantly improve the unsatisfiability-based algorithm for different benchmark sets.
This work was partially supported by FCT under research projects iExplain (PTDC/EIA-CCO/102077/2008) and ASPEN (PTDC/EIA-CCO/110921/2009), and INESC-ID multiannual funding through the PIDDAC program funds (PEst-OE/EEI/LA0021/2011).
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
Coudert, O.: On Solving Covering Problems. In: Proceedings of the Design Automation Conference, pp. 197–202 (June 1996)
Martins, R., Manquinho, V., Lynce, I.: On Partitioning for Maximum Satisfiability. In: European Conference on Artificial Intelligence, pp. 913–914 (2012)
Fu, Z., Malik, S.: On Solving the Partial MAX-SAT Problem. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 252–265. Springer, Heidelberg (2006)
Ansótegui, C., Bonet, M.L., Levy, J.: Solving (Weighted) Partial MaxSAT through Satisfiability Testing. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 427–440. Springer, Heidelberg (2009)
Manquinho, V., Marques-Silva, J., Planes, J.: Algorithms for Weighted Boolean Optimization. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 495–508. Springer, Heidelberg (2009)
Ansótegui, C., Bonet, M., Levy, J.: A New Algorithm for Weighted Partial MaxSAT. In: AAAI Conference on Artificial Intelligence, pp. 3–8 (2010)
Heras, F., Morgado, A., Marques-Silva, J.: Core-Guided Binary Search Algorithms for Maximum Satisfiability. In: AAAI Conference on Artificial Intelligence, pp. 36–41 (2011)
Janota, M., Lynce, I., Manquinho, V., Marques-Silva, J.: PackUp: Tools for Package Upgradability Solving. Journal on Satisfiability, Boolean Modeling and Computation 8(1/2), 89–94 (2012)
Li, C.M., Manyà, F.: MaxSAT, Hard and Soft Constraints. In: Handbook of Satisfiability, pp. 613–631. IOS Press (2009)
Koshimura, M., Zhang, T., Fujita, H., Hasegawa, R.: QMaxSAT: A Partial Max-SAT Solver. Journal on Satisfiability, Boolean Modeling and Computation 8, 95–100 (2012)
Ansótegui, C., Bonet, M.L., Gabàs, J., Levy, J.: Improving SAT-Based Weighted MaxSAT Solvers. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 86–101. Springer, Heidelberg (2012)
Park, T.J., Gelder, A.V.: Partitioning Methods for Satisfiability Testing on Large Formulas. Information and Computation 162(1-2), 179–184 (2000)
Karypis, G., Aggarwal, R., Kumar, V., Shekhar, S.: Multilevel hypergraph partitioning: Application in VLSI domain. IEEE Transactions on VLSI Systems 7, 69–79 (1999)
Ansótegui, C., Giráldez-Cru, J., Levy, J.: The Community Structure of SAT Formulas. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 410–423. Springer, Heidelberg (2012)
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proceedings of the National Academy of Sciences 99(12), 7821–7826 (2002)
Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Physical Review E 69(026113) (2004)
Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., Parisi, D.: Defining and identifying communities in networks. Proceedings of the National Academy of Sciences of the United States of America 101(9), 2658–2663 (2004)
Brandes, U., Delling, D., Gaertler, M., Goerke, R., Hoefer, M., Nikoloski, Z., Wagner, D.: Maximizing modularity is hard. arXiv: physics, 0608255 (2006)
Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Physical Review E 70(6), 066111 (2004)
Pons, P., Latapy, M.: Computing Communities in Large Networks Using Random Walks. Journal of Graph Algorithms and Applications 10(2), 191–218 (2006)
Blondel, V., Guillaume, J., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. Journal of Statistical Mechanics 2008(10), P10008 (2008)
Morgado, A., Marques-Silva, J.: Combinatorial Optimization Solutions for the Maximum Quartet Consistency Problem. Fundamenta Informaticae 102(3-4), 363–389 (2010)
Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: PBS: A backtrack search pseudo Boolean solver. In: Symposium on the Theory and Applications of Satisfiability Testing, pp. 346–353 (2002)
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
Martins, R., Manquinho, V., Lynce, I. (2013). Community-Based Partitioning for MaxSAT Solving. 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_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-39071-5_14
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)