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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 constraint is a way to describe different characteristics of values. A shape will contain one or more constraint declarations. SHACL provides many pre-built constraint types. For example, sh:datatype is used to describe the type of literal values e.g., if they are strings or integers or dates.
Under this definition, the constraint graph can have as many as () edges, where n is the number of blocks. Therefore, other, less dense constraint graphs are considered. The horizontal visibility graph is a horizontal constraint graph in which the horizontal constraint between two blocks exists only if there is a horizontal line segment which ...
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.
The constraint passed along an edge "summarizes" the effects of all constraints of the part of the graph on one side of the edge to the other one. The constraint passed from node i to node j summarizes the effects of the nodes on the "side" of i to the variables of j. In a tree, every edge breaks the graph in two parts.
Overview of a data-modeling context: Data model is based on Data, Data relationship, Data semantic and Data constraint. A data model provides the details of information to be stored, and is of primary use when the final product is the generation of computer software code for an application or the preparation of a functional specification to aid a computer software make-or-buy decision.
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]
A factor graph is a bipartite graph representing the factorization of a function. In probability theory and its applications, factor graphs are used to represent factorization of a probability distribution function , enabling efficient computations, such as the computation of marginal distributions through the sum–product algorithm .