Probabilistic analysis of set operations with constant-time set equality test

Abstract

We analyze the implementation of set operations using binary tries. Our techniques are substantially simpler than previous techniques used for this problem, and allow us to analysis not only the expected performance but also the probability distribution of the performance. We show that by making use of constant-time equality tests, we can achieve better performance than any previously known method for performing set operations. In particular, for two sets A and B of n elements that differ in only k elements, we can perform any set operation such as A ⋂ B in only O(k log n) expected time (without knowing in advance anything about the differences between A and B).