Abstract
(Soft) Constraint Satisfaction Problems (SCSPs) are expressive and well-studied formalisms to represent and solve constraint-satisfaction and optimization problems. A variety of algorithms to tackle them have been studied in the last 45 years, many of them based on dynamic programming. A limit of SCSPs is its lack of compositionality and, consequently, it is not possible to represent problem decompositions in the formalism itself. In this paper we introduce Soft Constraint Evaluation Problems (SCEPs), an algebraic framework, generalizing SCSPs, which allows for the compositional specification and resolution of (soft) constraint-based problems. This enables the systematic derivation of efficient dynamic programming algorithms for any such problem.
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Notes
- 1.
Width is conventionally defined as \(\max _{t \in T} \{ | X_t | \} - 1\). We drop “\(-1\)” so that it gives the actual number of parameters.
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Acknowledgements
We thank Nicklas Hoch and Giacoma Valentina Monreale for their collaboration in an earlier version of this work. We also thank an anonymous reviewer for suggesting the example where bucket elimination does not produce a canonical term.
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Montanari, U., Sammartino, M., Tcheukam, A. (2018). Decomposition Structures for Soft Constraint Evaluation Problems: An Algebraic Approach. In: Heckel, R., Taentzer, G. (eds) Graph Transformation, Specifications, and Nets. Lecture Notes in Computer Science(), vol 10800. Springer, Cham. https://doi.org/10.1007/978-3-319-75396-6_10
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