A Knowledge Compilation Map for Ordered Real-Valued Decision Diagrams

Hélène Fargier (1, 2) , Pierre Marquis (3) , Alexandre Niveau (4) , Nicolas Schmidt (1, 5, 3)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 CNRS - Centre National de la Recherche Scientifique
3 CRIL - Centre de Recherche en Informatique de Lens
4 GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen
5 UT3 - Université Toulouse III - Paul Sabatier

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.

Mots clés: Knowledge compilation; Decision diagram; Complexity; ADD; SLDD; AADD

Domaines: Intelligence artificielle [cs.AI]; Informatique et langage [cs.CL]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]

Hélène Fargier, Pierre Marquis, Alexandre Niveau, Nicolas Schmidt. A Knowledge Compilation Map for Ordered Real-Valued Decision Diagrams. 28th Conference on Artificial Intelligence (AAAI 2014), AAAI, Jul 2014, Quebec, Canada. pp.1049--1055. ⟨hal-04077580⟩