Abstract
Encoding to SAT and applying a highly efficient modern SAT solver is an increasingly popular method of solving finite-domain constraint problems. In this paper we study encodings of arbitrary constraints where unit propagation on the encoding provides strong reasoning. Specifically, unit propagation on the encoding simulates generalised arc consistency on the original constraint. To create compact and efficient encodings we use the concept of short support. Short support has been successfully applied to create efficient propagation algorithms for arbitrary constraints. A short support of a constraint is similar to a satisfying tuple however a short support is not required to assign every variable in scope. Some variables are left free to take any value. In some cases a short support representation is smaller than the table of satisfying tuples by an exponential factor. We present two encodings based on short supports and evaluate them on a set of benchmark problems, demonstrating a substantial improvement over the state of the art.
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Notes
- 1.
The set of short supports depends on the domains \(D_s\). We always use the initial domains. Elsewhere, short supports are generated using the current domains D but these sets are not necessarily short supports after backtracking [18, 19]. A support of either type is valid iff all literals in it are valid.
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Acknowledgements
We would like to thank the EPSRC for funding this work through grants EP/H004092/1, EP/K015745/1, and EP/M003728/1. In addition, Dr Jefferson is funded by a Royal Society University Research Fellowship.
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Akgün, Ö., Gent, I.P., Jefferson, C., Miguel, I., Nightingale, P. (2016). Exploiting Short Supports for Improved Encoding of Arbitrary Constraints into SAT. In: Rueher, M. (eds) Principles and Practice of Constraint Programming. CP 2016. Lecture Notes in Computer Science(), vol 9892. Springer, Cham. https://doi.org/10.1007/978-3-319-44953-1_1
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