Abstract
We analyze the complexity of optimization problems expressed using valued constraints. This very general framework includes a number of well-known optimization problems such as MAX-SAT, and Weighted MAX-SAT, as well as properly generalizing the classical CSP framework by allowing the expression of preferences. We focus on valued constraints over Boolean variables, and we establish a dichotomy theorem which characterizes the complexity of any problem involving a fixed set of constraints of this kind.
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References
Bistarelli, S., Fargier, H., Montanari, U., Rossi, F., Schiex, T., Verfaillie, G.: Semiring-based CSPs and valued CSPs: Frameworks, properties, and comparison. Constraints 4, 199–240 (1999)
Creignou, N., Khanna, S., Sudan, M.: Complexity Classification of Boolean Constraint Satisfaction Problems. In: Society for Industrial and Applied Mathematics. SIAM Monographs on Discrete Mathematics and Applications, vol. 7 (2001)
Schaefer, T.: The complexity of satisfiability problems. In: Proceedings 10th ACM Symposium on Theory of Computing, STOC 1978, pp. 216–226 (1978)
Cohen, D., Cooper, M., Jeavons, P., Krokhin, A.: Soft constraints: complexity and multimorphisms. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 244–258. Springer, Heidelberg (2003)
Bulatov, A., Krokhin, A., Jeavons, P.: Constraint satisfaction problems and Finite algebras. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. Bulatov, A., Krokhin, A., Jeavons, P, vol. 1853, pp. 272–282. Springer, Heidelberg (2000)
Jeavons, P., Cohen, D., Gyssens, M.: Closure properties of constraints. Journal of the ACM 44, 527–548 (1997)
Jeavons, P.: On the algebraic structure of combinatorial problems. Theoretical Computer Science 200, 185–204 (1998)
Pöschel, R., Kalužnin, L.: Funktionen- und Relationenalgebren. DVW, Berlin (1979)
Nemhauser, G., Wolsey, L.: Integer and Combinatorial Optimization. John Wiley & Sons, Chichester (1988)
Jeavons, P., Cohen, D., Cooper, M.: Constraints, consistency and closure. Artificial Intelligence 101, 251–265 (1998)
Iwata, S.: A faster scaling algorithm for minimizing submodular functions. SIAM Journal on Computing 32, 833–840 (2003)
Cohen, D., Cooper, M., Jeavons, P., Krokhin, A.: An investigation of the multimorphisms of tractable and intractable classes of valued constraints. Technical Report CSD-TR-03-03, CS department, Royal Holloway, University of London (2003)
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Cohen, D., Cooper, M., Jeavons, P. (2004). A Complete Characterization of Complexity for Boolean Constraint Optimization Problems. In: Wallace, M. (eds) Principles and Practice of Constraint Programming – CP 2004. CP 2004. Lecture Notes in Computer Science, vol 3258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30201-8_18
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DOI: https://doi.org/10.1007/978-3-540-30201-8_18
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