函数依赖图的理论及应用

Theory and Application of Functional Dependency Graph

本文提出函数依赖图的概念和理论,并重点应用它对关系模式候选关键字的求解问题进行了深入而系统的讨论,解决了单属性情况下候选关键字的求解问题,得到了若干新的结论。

The concept of Functional Dependency Graph (FDG) is proposed and used for solving the candidate key in the case of single attribute dependency set. The following conclusions are drawn:a. If there is a key attribute node in FDG, then the key attribute will definitely be included in all candidate ksys of R, where R is the node of relation;b. If there is no independent loop in FDG, then the key attribute set will be the unique candidate key of R;c. If there are k independent loops (k≥1) in FDG, then R has m (m>1) candidate keys with each containing n attributes composed of two parts, i.e., the key attribute set and the selected attribute set. The former will be found in all candidate keys while the latter can only be found in one candidate key from an indpendent loop. In addition, if X represents a key attribute set, n1, …, nk the numbers of the nodes of independent loops respectively, then m = n1 n2…nk, n = |x| + k. This means that n is a constant.