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In constraint satisfaction research in artificial intelligence and operations research, constraint graphs and hypergraphs are used to represent relations among constraints in a constraint satisfaction problem. A constraint graph is a special case of a factor graph, which allows for the existence of free variables.
A graph with a system of edge weights and vertex thresholds is called a constraint graph. The restricted case where the edge weights are all one or two, the vertices require two units of incoming weight, and the vertices all have three incident edges with an even number of red edges, are called and/or constraint graphs. [2]
The classic model of Constraint Satisfaction Problem defines a model of static, inflexible constraints. This rigid model is a shortcoming that makes it difficult to represent problems easily. [ 33 ] Several modifications of the basic CSP definition have been proposed to adapt the model to a wide variety of problems.
A possible definition of constraint graphs is as follows. The constraint graph for a given floorplan is a directed graph with vertex set being the set of floorplan blocks and there is an edge from block b1 to b2 (called horizontal constraint), if b1 is completely to the left of b2 and there is an edge from block b1 to b2 (called vertical ...
A similar definition can be given for a constraint satisfaction problem using its primal graph. The width of a cycle decomposition is the number of variables in the cutset. The width of a problem is the minimal width of its cycle cutset decompositions.
Constraint satisfaction problems composed of binary constraints only can be viewed as graphs, where the vertices are variables and the edges represent the presence of a constraint between two variables. This graph is called the Gaifman graph or primal constraint graph (or simply primal graph) of the problem.
Learning constraints representing these partial evaluation is called graph-based learning. It uses the same rationale of graph-based backjumping. These methods are called "graph-based" because they are based on pairs of variables in the same constraint, which can be found from the graph associated to the constraint satisfaction problem.
Constraint toolkits are a way for embedding constraints into an imperative programming language. However, they are only used as external libraries for encoding and solving problems. An approach in which constraints are integrated into an imperative programming language is taken in the Kaleidoscope programming language.