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Nicolas Schmidt

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AAAI Conference 2014 Conference Paper

A Knowledge Compilation Map for Ordered Real-Valued Decision Diagrams

Hélène Fargier
Pierre Marquis
Alexandre Niveau
Nicolas Schmidt

Valued decision diagrams (VDDs) are data structures that represent functions mapping variable-value assignments to non-negative real numbers. They prove useful to compile cost functions, utility functions, or probability distributions. While the complexity of some queries (notably optimization) and transformations (notably conditioning) on VDD languages has been known for some time, there remain many significant queries and transformations, such as the various kinds of cuts, marginalizations, and combinations, the complexity of which has not been identified so far. This paper contributes to filling this gap and completing previous results about the time and space efficiency of VDD languages, thus leading to a knowledge compilation map for real-valued functions. Our results show that many tasks that are hard on valued CSPs are actually tractable on VDDs.

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IJCAI Conference 2013 Conference Paper

Semiring Labelled Decision Diagrams, Revisited: Canonicity and Spatial Efficiency Issues

Hélène Fargier
Pierre Marquis
Nicolas Schmidt

Existing languages in the valued decision diagrams (VDDs) family, including ADD, AADD, and those of the SLDD family, prove to be valuable target languages for compiling multivariate functions. However, their efficiency is directly related to the size of the compiled formulae. In practice, the existence of canonical forms may have a major impact on the size of the compiled VDDs. While efficient normalization procedures have been pointed out for ADD and AADD the canonicity issue for SLDD formulae has not been addressed so far. In this paper, the SLDD family is revisited. We modify the algebraic requirements imposed on the valuation structure so as to ensure tractable conditioning, optimization and normalization for some languages of the revisited SLDD family. We show that AADD is captured by this family. Finally, we compare the spatial efficiency of some languages of this family, from both the theoretical side and the practical side.

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