Use Closure of Relevant Sets of Attributes to Efficiently Find Candidate Keys

Based on canonical cover or minimum cover for functional dependency set F, a data structure MAC is constructed, which facilitates to compute closures of all attributes sets. Using MAC, a fast algorithm of computing closure of an individual set of attributes is improved to efficiently find candidate keys. The improved algorithm of finding candidate keys neednpsilat compute closures of the total subsets of R, but compute closures of the subsets which are closely relevant to candidate keys, namely, which are candidate keys or one part of candidate keys. Based on the improved algorithm for fast computing closures of the sets of attributes in left set and theorem of reference, an efficient algorithm of finding the total candidate keys are gained, whose time complexity is O(nmiddot|R|middot|F_c|²).