Breaking Symmetries with RootClique and LexTopSort

Bounded fractional hypertree width is the most general known structural property that guarantees polynomial-time solvability of the constraint satisfaction problem. Fichte et al. (CP 2018) presented a robust and scalable method for finding optimal fractional hypertree decompositions, based on an encoding to SAT Modulo Theory (SMT). In this paper, we provide an in-depth study of two powerful symmetry breaking predicates that allow us to further speed up the SMT-based decomposition: RootClique fixes the root of the decomposition tree; LexTopSort fixes the elimination ordering with respect to an underlying DAG. We perform an extensive empirical evaluation of both symmetry-breaking predicates with respect to the primal graph (which is known in advance) and the induced graph (which is generated during the search).

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