Compiling constraint networks into AND/OR multi-valued decision diagrams (AOMDDs)

Inspired by AND/OR search spaces for graphical models recently introduced, we propose to augment Ordered Decision Diagrams with AND nodes, in order to capture function decomposition structure. This yields AND/OR multivalued decision diagram (AOMDD) which compiles a constraint network into a canonical form that supports polynomial time queries such as solution counting, solution enumeration or equivalence of constraint networks. We provide a compilation algorithm based on Variable Elimination for assembling an AOMDD for a constraint network starting from the AOMDDs for its constraints. The algorithm uses the APPLY operator which combines two AOMDDs by a given operation. This guarantees the complexity upper bound for the compilation time and the size of the AOMDD to be exponential in the treewidth of the constraint graph, rather than pathwidth as is known for ordered binary decision diagrams (OBDDs)