An itemset \(X\) is called a generator on a data set \(D\) if there does not exist a proper subitemset \(Y \subset\) \(X\) such that \(\operatorname{support}(X)=\operatorname{support}(Y)\). A generator \(X\) is a frequent generator if \(\operatorname{support}(X)\) passes the minimum support threshold. Let \(\mathcal{G}\) be the set of all frequent generators on a data set \(D\).

a. Can you determine whether an itemset \(A\) is frequent and the support of \(A\), if it is frequent, using only \(\mathcal{G}\) and the support counts of all frequent generators? If yes, present your algorithm. Otherwise, what other information is needed? Can you give an algorithm assuming the information needed is available?

b. What is the relationship between closed itemsets and generators?