Exploiting Symmetry in Lifted CSPs

David Joslin, Amitabha Roy

When search problems have large-scale symmetric structure, detecting and exploiting that structure can greatly reduce the size of the search space. Previous work has shown how to find and exploit symmetries in propositional encodings of constraint satisfaction problems (CSPs). Here we consider problems that have more compact "lifted" (quantified) descriptions from which propositional encodings can be generated. We describe an algorithm for finding symmetries in lifted representations of CSPs, and show sufficient conditions under which these symmetries can be mapped to symmetries in the propositional encoding. Using two domains (pigeonhole problems, and a CSP encoding of planning problems), we demonstrate experimentally that the approach of finding symmetries in lifted problem representations is a significant improvement over previous approaches that find symmetries in propositional encodings.

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