An output sensitive solution to the set union and intersection problem

Abstract

In this paper we propose an alternative approaches for the efficient solution of the set union and intersection problem, a variant of the classical disjoint set union problem, in which two distinct sequences of unions are simultaneously performed on two distinct collections of n singletons. In this context, it makes sense to introduce a new operation, named findint(x), that, given an element x, returns the intersection of the two sets containing x in both collections. We use a new data structures called intersection lists that reaches the optimal Θ(p) worst case time for executing a findint operation, where p is the size of the output, and spends O(n) worst case time for a union and O(1) worst case time for a find operation.