Abstract
In this paper we present an efficient way to encode connectedness in reductions from graph problems to SAT and MaxSAT. We show and prove linear reductions from Minimum Path and Clique and a quadratic reduction from Steiner Tree, although others NP-complete and NP-hard problems can be reduced with this complexity as well. These reductions use a new class of operators that extends the traditional set of connectors of propositional logic.
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References
Kautz, H., Selman, B., Jiang, Y.: A General Stochastic Approach to Solving Problems with Hard and Soft Constraints. In: The Satisfiability Problem – Theory and Applications, pp. 573–586. American Mathematical Society (1996)
Menai, M.E.B.: A Logic-Based Approach to Solve the Steiner Tree Problem. In: Iliadis, Maglogiann, Tsoumakasis, Vlahavas, Bramer (eds.) Artificial Intelligence Applications and Innovations III. IFIP AICT, vol. 296, pp. 73–79. Springer, Heidelberg (2009)
Heras, F., Larrosa, J., Oliveras, A.: Minimaxsat – An Efficient Weighted Max-Sat Solver. Journal of Artificial Intelligence Research 31(1), 1–32 (2008)
Muller, D.E., Preparata, F.P.: Bounds to Complexities of Networks for Sorting and for Switching. Journal of the ACM 22(2), 195–201 (1975)
Karp, R.M.: Reducibility Among Combinatorial Problems. In: Complexity of Computer Computations, pp. 85–103. Plenum Press (1972)
Koch, T., Martin, A., Vos, S.: Steinlib: An Updated Library on Steiner Tree Problems in Graphs. Technical Report ZIB 00-37. Zuse Institute Berlin (2000)
Biere, A.: Lingeling, Plingeling, Picosat and Precosat at SAT race 2010. Technical Report 10/1, FMV Reports Series. Institute for Formal Models and Verification, Johannes Kepler University (2010)
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Tavares de Oliveira, R., Silva, F., Ribas, B.C., Castilho, M.A. (2012). On Modeling Connectedness in Reductions from Graph Problems to Extended Satisfiability. In: Pavón, J., Duque-Méndez, N.D., Fuentes-Fernández, R. (eds) Advances in Artificial Intelligence – IBERAMIA 2012. IBERAMIA 2012. Lecture Notes in Computer Science(), vol 7637. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34654-5_39
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DOI: https://doi.org/10.1007/978-3-642-34654-5_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34653-8
Online ISBN: 978-3-642-34654-5
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