A constraint satisfaction problem (CSP) involves a set of variables, a domain of potential values for each variable, and a set of constraints, which specifies the acceptable combinations of values. One popular approach is to represent the original problem as a constraint network where nodes represent variables and arcs represent constraints between variables. Node consistency and arc consistency techniques are first applied to prune the domains of variables. Constraint propagation techniques are then applied to solve the problem. Many AI and engineering problems can be formulated as CSPs and solved by various CSP algorithms such as constraint propagation, backtracking, forward checking, and hybrids. This paper gives an overview of these algorithms. In particular, we present a review of the interval constraint satisfaction problems (ICSP). Real intervals or sets of discrete values label the variables. The constraints can be binary relationships or n-ary mathematical operations. The techniques for solving the interval constraint satisfaction problem such as Waltz filtering and tolerance propagation are presented.
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