The Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18) Parallel Algorithms for Operations on Multi-Valued Decision Diagrams Guillaume Perez Jean-Charles Regin´ Dept. of Computer Science Universit Nice Sophia Antipolis, CNRS, I3S Cornell University, Ithaca, NY 14850 USA UMR 7271, 06900 Sophia Antipolis, France
[email protected] [email protected] Abstract constraints represented by MDDs correspond to operations performed on MDDs. Conjunction of constraints is accom- Multi-valued Decision Diagrams (MDDs) have been exten- plished by intersecting MDDs and disjunction by union. sively studied in the last ten years. Recently, efficient algo- rithms implementing operators such as reduction, union, in- Recently, efficient operators such as union, difference tersection, difference, etc., have been designed. They directly negation, intersection, etc., have been designed (Perez and deal with the graph structure of the MDD and a time reduction Regin´ 2015; 2016). These are based on algorithms dealing of several orders of magnitude in comparison to other existing directly with the graph structure of the MDD instead of func- algorithms have been observed. These operators have permit- tion decomposition, which requires reaching the leaves of ted a new look at MDDs, because extremely large MDDs can a branch as Shannon or Bryant did (Bryant 1986). By ex- finally be manipulated as shown by the models used to solve plicitly working on the structure, they dramatically accel- complex application in music generation. However, MDDs erated the algorithm and observed a time reduction of sev- become so large (50GB) that minutes are sometimes required eral orders of magnitude in comparison to other existing al- to perform some operations.