A Generalized Parallel Algorithm for Frequent Itemset Mining

A parallel algorithm for finding the frequent itemsets in a set of transactions is presented. The frequent individual items are identified by their index. We assume that processors number (m) is less than the frequent items number (n). At the first stage, every processor P-i, i epsilon {1,..., m - 1} sequentially computes the frequent itemsets from the interval I-i = [(i - 1) . p + 1, i . p], where p = [n/m]. The processor P-m computes frequent M itemsets from the interval I-m = [(m - 1) . p + 1, n]. In the second stage, the parallel algorithm is applied. The processor P-i computes, step by step, the sets F-Ii,F-Ij of the frequent itemsets with individual items from the intervals I-i,I-j = I-i boolean OR Ii+1 boolean OR....boolean OR I-j,I- j = i + 1,...m. In order to compute the set F-Ii,F-Ij, the processor P-i uses F-Ii,F-Ij-1 obtained in the previous step and F-Ii+1,F-Ij received from the processor Pi+1. The main advantage of our parallel algorithm is that it uses a communication pattern known before algorithm start, which permits to map the communication to hardware. Another major advantage is that the set of the transactions can be distributed to processors before the beginning of the algorithm. This is possible because a processor Pi has to compute F-Ii,F-Ij,F-j = i + 1,..., m and therefore only the transactions containing the frequent items starting with I-i are needed.