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On Modeling Connectedness in Reductions from Graph Problems to Extended Satisfiability

by: Ricardo Tavares de Oliveira, Fabiano Silva, BrunoCesar Ribas, MarcosA Castilho

edited by: Juan Pavón, NéstorD Duque-Méndez, Rubén Fuentes-Fernández

In Advances in Artificial Intelligence – IBERAMIA 2012, Vol. 7637 (2012), pp. 381-391, doi:10.1007/978-3-642-34654-5_39  Key: citeulike:12069973

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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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