Decision diagrams : constraints and algorithms

Abstract : Multivalued Decision Diagrams (MDDs) are efficient data structures widely used in several fields like verification, optimization and dynamic programming. In this thesis, we first focus on improving the main algorithms such as the reduction, allowing MDDs to potentially exponentially compress set of tuples, or the combination of MDDs such as the intersection of the union. We go further by designing parallel algorithms, and algorithms handling non-deterministic MDDs. We then investigate relaxed MDDs, that are more and more used in optimization, and define the notions of relaxed reduction or operation and design efficient algorithms for them. The sampling of solutions stored in a MDD is solved with respect to probability mass functions or Markov chains. In order to combine MDDs with constraint Programming, we design the propagators of all the types of MMDD constraints in solvers, and introduce a new one, the channeling constraint. These new propagators outperform the existing ones and allow the reformulation of several other constraints such as the dispersion constraint, and even to define new ones easily. We finally apply our algorithm to several real world industrial problems such as text and music generation and geomodeling of a petroleum reservoir.
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Guillaume Perez. Decision diagrams : constraints and algorithms. Other [cs.OH]. Université Côte d'Azur, 2017. English. ⟨NNT : 2017AZUR4081⟩. ⟨tel-01677857⟩

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