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Boosting MUS Extraction

  • Conference paper
Abstraction, Reformulation, and Approximation (SARA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4612))

Abstract

If a CSP instance has no solution, it contains a smaller unsolvable subproblem that makes unsolvable the whole problem. When solving such instance, instead of just returning the “no solution” message, it is of interest to return an unsolvable subproblem. The detection of such unsolvable subproblems has many applications: failure explanation, error diagnosis, planning, intelligent backtracking, etc. In this paper, we give a method for extracting a Minimal Unsolvable Subproblem (MUS) from a CSP based on a Forward Checking algorithm with Dynamic Variable Ordering (FC-DVO). We propose an approach that improves existing techniques using a two steps algorithm. In the first step, we detect an unsolvable subproblem selecting a set of constraints, while in the second step we refine this unsolvable subproblem until a MUS is obtained. We provide experimental results that show how our approach improves other approaches based on MAC-DVO algorithms.

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References

  1. Bailey, J., Stuckey, P.J.: Discovery of Minimal Unsatisfiable Subsets of Constraints Using Hitting Set Dualization. In: Hermenegildo, M.V., Cabeza, D. (eds.) Practical Aspects of Declarative Languages. LNCS, vol. 3350, pp. 174–186. Springer, Heidelberg (2005)

    Google Scholar 

  2. Benchmark problems. http://cpai.ucc.ie/05/Benchmarks.html

  3. Bruni, R.: Approximating minimal unsatisfiable subformulae by means of adaptive core search. Discrete App. Math. Journal, vol. 130, pp. 85–100. Elsevier Science Publishers, BV (2003)

    Google Scholar 

  4. Bruni, R., Sassano, A.: Restoring Satisfiability or Maintaining Unsatisfiability by Finding Small Unsatisfiable Subformulae. In: Bruni, R., Sassano, A. (eds.) SAT 2001 (LICS) 2001 Workshop on Theory and Applications of Satisfiability Testing, Boston, Massachusetts, USA, June 14-15, 2001, pp. 14–15. Elsevier Science Pub., North-Holland, Amsterdam (2001)

    Google Scholar 

  5. Faltings, B., Macho-Gonzalez, S.: Open Constraint Programming. Artificial Intelligence, vol 161, pp. 181–208 (2005)

    Google Scholar 

  6. Freuder, E., Hubbe, P.: Extracting Constraint Satisfaction Subproblems. In: Proc. of the 14th International Joint Conference on Artificial Intelligence. pp. 548–555 (1995)

    Google Scholar 

  7. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)

    MATH  Google Scholar 

  8. Ginsberg, M.L.: Dynamic backtracking. Journal of Artificial Intelligence Research 1, 25–46 (1993)

    MATH  Google Scholar 

  9. Haralick, R., Elliot, G.: Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence 14, 263–313 (1980)

    Article  Google Scholar 

  10. Hemery, F., Lecoutre, C., Sais, L., Boussemart, F.: Extracting MUCs from constraint networks. In: ECAI 2006. Proceedings of the 17th European Conference on Artificial Intelligence (2006)

    Google Scholar 

  11. Huang, J.: MUP: a minimal unsatisfiability prover. In: Huang, J. (ed.) ASP-DAC 2005. Proceedings of the 2005 conference on Asia South Pacific design automation, Shanghai, China, pp. 432–437. ACM Press, NewYork (2005)

    Chapter  Google Scholar 

  12. Java Constraint Library (JCL): http://liawww.epfl.ch/JCL/

  13. Junker, U.: QUICKXPLAIN: Conflict Detection for Arbitrary Constraint Propagation Algorithms. In: IJCAI 2001 Workshop on Modelling and Solving problems with constraints (CONS-1) (2001)

    Google Scholar 

  14. Kar, R.M.: Reducibility among combinatorial problems. Complexity of Computer Computations, pp. 85–103 (1972)

    Google Scholar 

  15. Liffiton, M.H., Andraus, Z.S., Sakallah, K.A.: From Max-SAT to Min-UNSAT: Insights and Applications. Technical Report CSE-TR-506-05 (February 2005)

    Google Scholar 

  16. Liffiton, M.H., Moffitt, M.D., Pollack, M.E., Sakallah, K.A.: Identifying Conflicts in Overconstrained Temporal Problems. In: Proc. IJCAI 2005, pp. 205–211, Edinburgh, Scotland (2005)

    Google Scholar 

  17. Liffiton, M.H., Sakallah, K.A.: On Finding All Minimally Unsatisfiable Subformulas. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 173–186. Springer, Heidelberg (2005)

    Google Scholar 

  18. Oh, Y., Mneimneh, M.N., Andraus, Z.S., Sakallah, K.A., Markov, I.L.: AMUSE: a minimally-unsatisfiable subformula extractor. In: DAC 2004. Proceedings of the 41st annual conference on Design automation, pp. 518–523. ACM Press, New York (2004)

    Chapter  Google Scholar 

  19. Prosser, P.: Hybrid algorithms for the constraint satisfaction problem. Computational Intelligence 9, 268–299 (1993)

    Article  Google Scholar 

  20. Torrens, M., Weigel, R., Faltings, B.: Java constraint library: Bringing constraints technology on the Internet using the java language. In: Constraints and Agents: Papers from the 1997 AAAI Workshop, Menlo Park, California, pp. 21–25 (1997)

    Google Scholar 

  21. Verfaillie, G., Lemaitre, M., Schiex, T.: Russian Doll Search. In: Proc. of the 13th National Conference on Artificial Intelligence, pp. 181–187 (1996)

    Google Scholar 

  22. Yokoo, M.: Asynchronous weak-commitment search for solving distributed constraint satisfaction problems. In: Montanari, U., Rossi, F. (eds.) CP 1995. LNCS, vol. 976, pp. 88–102. Springer, Heidelberg (1995)

    Google Scholar 

  23. Zhang, L., Malik, S.: Extracting small unsatisfiable cores from unsatisfiable Boolean formula. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, Springer, Heidelberg (2004)

    Google Scholar 

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Authors and Affiliations

  1. IIIA, Institut d’Investigació en Intel.ligència Artificial, CSIC, Consejo Superior de Investigaciones Científicas, Campus UAB, 08193 Bellaterra, Catalonia, Spain

    Santiago Macho González & Pedro Meseguer

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  1. Santiago Macho González
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  2. Pedro Meseguer
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Ian Miguel Wheeler Ruml

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Macho González, S., Meseguer, P. (2007). Boosting MUS Extraction. In: Miguel, I., Ruml, W. (eds) Abstraction, Reformulation, and Approximation. SARA 2007. Lecture Notes in Computer Science(), vol 4612. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73580-9_23

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  • DOI: https://doi.org/10.1007/978-3-540-73580-9_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73579-3

  • Online ISBN: 978-3-540-73580-9

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