AND/OR Multi-valued Decision Diagrams for Constraint Networks

The paper is an overview of a recently developed compilation data structure for graphical models, with specific application to constraint networks. The AND/OR Multi-Valued Decision Diagram (AOMDD) augments well known decision diagrams (OBDDs, MDDs) with AND nodes, in order to capture function decomposition structure. The AOMDD is based on a pseudo tree of the network, rather than a linear ordering of its variables. The AOMDD of a constraint network is a canonical form given a pseudo tree. We describe two main approaches for compiling the AOMDD of a constraint network. The first is a top down, search-based procedure, that works by applying reduction rules to the trace of the memory intensive AND/OR search algorithm. The second is a bottom up, inference-based procedure, that uses a Bucket Elimination schedule. For both algorithms, the compilation time and the size of the AOMDD are, in the worst case, exponential in the treewidth of the constraint graph, rather than pathwidth as is known for ordered binary decision diagrams (OBDDs).