Tractable Structures for Constraint Satisfaction Problems

Publisher Summary This chapter focuses on structure-driven constraint processing algorithms. It discusses that search in constraint satisfaction takes the form of depth-first backtracking, while inference is performed by variable-elimination and tree-clustering algorithms, or by bounded local consistency enforcing. Compared to human problem solving techniques, conditioning is analogous to guessing, or reasoning by assumption. On the other hand, inference corresponds to reinterpreting or making deduction from the problem at hand. Inference-based algorithms derive and record new information, generating equivalent problem representations that facilitate an easier solution. The chapter also reviews that inference algorithms shows their performance is controlled by graph parameters such as tree-width, induced-width and hypertree width. The chapter also discusses that hybrids of search and inference can be controlled by graph-based parameters such as cycle-cutset, and w-cutset and separator-size. It presents the notion of AND/OR search spaces for exploiting independencies displayed in the constraint graph during search, which, similar to inference, leads to graph-based performance bounds using parameters such as the depth of the pseudo-tree, path-width and tree-width.