SAT Modulo Graphs: Acyclicity

Acyclicity is a recurring property of solutions to many important combinatorial problems. In this work we study embeddings of specialized acyclicity constraints in the satisfiability problem of the classical propositional logic (SAT). We propose an embedding of directed graphs in SAT, with arcs labelled with propositional variables, and an extended SAT problem in which all clauses have to be satisfied and the subgraph consisting of arcs labelled true is acyclic. We devise a constraint propagator for the acyclicity constraint and show how it can be incorporated in off-the-shelf SAT solvers. We show that all existing encodings of acyclicity constraints in SAT are either prohibitively large or do not sanction all inferences made by the constraint propagator. Our experiments demonstrate the advantages of our solver over other approaches for handling acyclicity.