Constraint satisfaction is a simple but powerful tool. Constraints identify the impossible and reduce the realm of possibilities to effectively focus on the possible, allowing for a natural declarative formulation of what must be satisfied, without expressing how. The field of constraint reasoning has matured over the last three decades with contributions from a diverse community of researchers in artificial intelligence, databases and programming languages, operations research, management science, and applied mathematics. Today, constraint problems are used to model cognitive tasks in vision, language comprehension, default reasoning, diagnosis, scheduling, temporal and spatial reasoning.
In Constraint Processing, Rina Dechter, synthesizes these contributions, along with her own significant work, to provide the first comprehensive examination of the theory that underlies constraint processing algorithms. Throughout, she focuses on fundamental tools and principles, emphasizing the representation and analysis of algorithms.
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acyclic algebra applied arc-consistent relative Artificial Intelligence assignment backjumping backtrack-free backtracking search binary constraints binary network Boolean bound bounds-consistency bucket elimination Chapter clause cliques compute conflict set Consider constraint graph constraint language constraint network constraint problem constraint processing constraint propagation constraint satisfaction problems cutset cycle-cutset Dechter defined DEFINITION denoted dual graph elimination algorithm enforcing example exponential Figure finite domain forward-checking given globally consistent goal graph G graph-based backjumping heuristic hybrid hypergraph inconsistent indicator problem induced graph induced width inference Input instantiation integers intervals join-tree linear logic programming look-ahead maximal mini-bucket minimal network no-good nodes number of variables optimal ordered graph Output pair path-consistency polynomial primal graph procedure propositional random relational arc-consistency row convex satisfies scope search algorithm search space selected solved space complexity straint subproblem subset temporal THEOREM tractable languages tree decomposition tuple unit propagation variable elimination variable ordering variables x1 yields