Abstract
We describe a new algorithm for solving linear integer programming problems. The algorithm performs a DPLL style search for a feasible assignment, while using a novel cut procedure to guide the search away from the conflicting states.
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References
Achterberg, T.: SCIP: Solving constraint integer programs. PhD thesis, TU Berlin (2007)
Achterberg, T., Koch, T., Martin, A.: MIPLIB 2003. Operations Research Letters 34(4), 361–372 (2006)
Berre, D.L., Parrain, A.: The Sat4j library, release 2.2 system description. Journal on Satisfiability, Boolean Modeling and Computation 7, 59–64 (2010)
Chvátal, V.: Edmonds polytopes and a hierarchy of combinatorial problems. Discrete Mathematics 4(4), 305–337 (1973)
Cooper, D.: Theorem proving in arithmetic without multiplication. Machine Intelligence 7(91-99), 300 (1972)
Cotton, S.: Natural domain SMT: A preliminary assessment. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 77–91. Springer, Heidelberg (2010)
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Communications of the ACM 5(7), 397 (1962)
Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM (JACM) 7(3), 201–215 (1960)
de Moura, L., Bjørner, N.S.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)
Dillig, I., Dillig, T., Aiken, A.: Cuts from proofs: A complete and practical technique for solving linear inequalities over integers. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 233–247. Springer, Heidelberg (2009)
Dutertre, B., de Moura, L.: A Fast Linear-Arithmetic Solver for DPLL(T). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 81–94. Springer, Heidelberg (2006)
Gomory, R.E.: Outline of an algorithm for integer solutions to linear programs. Bulletin of the American Mathematical Society 64(5), 275–278 (1958)
Griggio, A.: A practical approach to SMT(LA(Z)). In: SMT Workshop (2010)
Korovin, K., Tsiskaridze, N., Voronkov, A.: Conflict resolution. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, Springer, Heidelberg (2009)
Krstic, S., Goel, A.: Architecting Solvers for SAT Modulo Theories: Nelson-Oppen with DPLL. In: FroCos (2007)
McMillan, K.L., Kuehlmann, A., Sagiv, M.: Generalizing DPLL to richer logics. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 462–476. Springer, Heidelberg (2009)
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: DAC (2001)
Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT Modulo Theories: From an abstract DPLL procedure to DPLL(T). J. ACM 53(6), 937–977 (2006)
Silva, J.P.M., Sakallah, K.A.: GRASP – a new search algorithm for satisfiability. In: ICCAD (1997)
Wolsey, L.A., Nemhauser, G.L.: Integer and combinatorial optimization. Wiley, New York (1999)
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Jovanović, D., de Moura, L. (2011). Cutting to the Chase Solving Linear Integer Arithmetic. In: Bjørner, N., Sofronie-Stokkermans, V. (eds) Automated Deduction – CADE-23. CADE 2011. Lecture Notes in Computer Science(), vol 6803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22438-6_26
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DOI: https://doi.org/10.1007/978-3-642-22438-6_26
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