Abstract
Multi-Valued Decision Diagrams (MDDs), and more generally Multi-Valued Variable Diagrams (MVDs), are instrumental in modeling constrained combinatorial problems. This has led to a number of algorithms for filtering constraints such as mddc, MDD4R and CD (Compact-Diagram). Many compressed forms of tables have also been proposed over the years, leading to a ‘smart’ hybridization between extensional an intentional representations, which was obtained by embedding simple arithmetic constraints in tuples (of tables). Interestingly, the state-of-the-art algorithm CT (Compact-Table) has been recently extended to deal efficiently with bs-tables, i.e., ‘basic smart’ tables containing expressions of the form ‘\(*\)’, ‘\(\not = v\)’, ‘\(\le v\)’, ‘\(\ge v\)’ and ‘\(\in S\)’. In this paper, we introduce the concept of bs-MVDs by enabling arcs of diagrams to be labelled with similar expressions. We show how such diagrams can be naturally derived from ordinary tables and MDDs, and we extend the state-of-the-art algorithm CD in order to handle bs-MVDs (and bs-MDDs).
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Notes
- 1.
In [27], a sparse-set domain implementation for obtaining \(\varDelta _x\) without overhead is described.
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The second author is supported by the project CPER Data from the “Hauts-de-France”.
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Verhaeghe, H., Lecoutre, C., Schaus, P. (2019). Extending Compact-Diagram to Basic Smart Multi-Valued Variable Diagrams. In: Rousseau, LM., Stergiou, K. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019. Lecture Notes in Computer Science(), vol 11494. Springer, Cham. https://doi.org/10.1007/978-3-030-19212-9_39
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