Apriori algorithms are popular data mining techniques for extracting association rules from a body of data. The computational complexity of these algorithms is reduced by representing itemset information at cells of a hypercube. The cells encode associations between the items of each transaction. Direct computation of a cell as a lexicographic combination of items accelerates the computation of itemsets, and thereby improves the computational runtime complexity of the apriori algorithm that discovers association rules. Even faster computation is achieved by a user selected cardinality that limits the maximum size of the itemsets.