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dependency graph : ウィキペディア英語版
dependency graph

In mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other. It is possible to derive an evaluation order or the absence of an evaluation order that respects the given dependencies from the dependency graph.
== Definition ==
right
Given a set of objects S and a transitive relation R \subseteq S \times S with (a,b) \in R modeling a dependency "a needs b evaluated first", the dependency graph is a graph G = (S, T) with T \subseteq R and R being the transitive closure of T.
For example, assume a simple calculator. This calculator supports assignment of constant values to variables and assigning the sum of exactly 2 variables to a third variable. Given several equations like "''A'' = ''B''+''C''; ''B'' = 5+''D''; ''C''=4; ''D''=2;", then S= and R=. You can derive this relation directly: ''A'' depends on ''B'' and ''C'', because you can add two variables if and only if you know the values of both variables. Thus, ''B'' and ''C'' must be calculated before ''A'' can be calculated. However, ''Ds value is known immediately, because it is a number literal.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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