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Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables , which is solved by constraint satisfaction methods.
Other considered kinds of constraints are on real or rational numbers; solving problems on these constraints is done via variable elimination or the simplex algorithm. Constraint satisfaction as a general problem originated in the field of artificial intelligence in the 1970s (see for example (Laurière 1978)).
An example constraint satisfaction problem; this problem is binary, and the constraints are represented by edges of this graph. A decomposition tree; for every edge of the original graph, there is a node that contains both its endpoints; all nodes containing a variable are connected
AC-3 operates on constraints, variables, and the variables' domains (scopes). A variable can take any of several discrete values; the set of values for a particular variable is known as its domain. A constraint is a relation that limits or constrains the values a variable may have. The constraint may involve the values of other variables.
The randomness helps min-conflicts avoid local minima created by the greedy algorithm's initial assignment. In fact, Constraint Satisfaction Problems that respond best to a min-conflicts solution do well where a greedy algorithm almost solves the problem. Map coloring problems do poorly with Greedy Algorithm as well as Min-Conflicts. Sub areas ...
In constraint satisfaction, local search is an incomplete method for finding a solution to a problem. It is based on iteratively improving an assignment of the variables until all constraints are satisfied. In particular, local search algorithms typically modify the value of a variable in an assignment at each step.
Constraint programming (CP) [1] is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state the constraints on the feasible solutions for a set of decision variables.
Within artificial intelligence and operations research for constraint satisfaction a hybrid algorithm solves a constraint satisfaction problem by the combination of two different methods, for example variable conditioning (backtracking, backjumping, etc.) and constraint inference (arc consistency, variable elimination, etc.)