Constraint programming

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Constraint Programming (CP) is a paradigm to solve satisfaction or optimization problems by a two-step approach: propagation and tree search. Given a CSP the decision variables’ domains are tightened by first propagating the constraints. If after this step all domains contain only one value then a solution has been found. If at least one domain is empty, the CSP has no solutions. Otherwise, the second step, tree search, is initiated: by specifying a variable ordering heuristic and a value ordering heuristic, a search tree is constructed which is then traversed according to one of various search strategies. If the problem is a satisfaction problem, the first solution found is returned or it is proved that no solution exists. For an optimization problem the whole tree is traversed in a branch-and-bound search and the best solution returned.

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