Efficient computation of frequent itemsets in a subcollection of multiple set families

Many applications need to deal with the additive and multiplicative subcollections over a group of set families (databases). This paper presents two efficient algorithms for computing the frequent itemsets in these two types of subcollections respectively. Let T be a given subcollection of set families of total size m whose elements are drawn from a domain of size n. We show that ifT is an additive subcollection we can compute all frequent itemsets in T in O(m2ⁿ/(pn) + log p) time on an EREW PRAM with 1 ≤ p ≤ m2ⁿ/n processors, at a cost of maintaining the occurrences of all itemsets in each individual set family. If T is a multiplicative subcollection, we can compute all itemsets in T in O(mk/p + min {m′/p 2ⁿ, n3ⁿ log m′/p}) time on an EREW PRAM with 1 ≤ p ≤ min {m,2ⁿ} processors, where m′ = min {m,2ⁿ}. These present improvements over direct computation of the frequent itemsets on the subcollection concerned.