A probabilistic distributed algorithm for set intersection and its analysis

Abstract

A probabilistic algorithm for checking set disjointness and performing set intersection of two sets stored in different machines is presented. The algorithm is intended to minimize the amount of communication between the machines. If n is the total number of elements and k is the number of bits required to represent each of the element, then it is shown that the expected running time of the set disjointness algorithm is O(log log n) rounds, each round consisting of exchanging one message with O(n + k) bits and performing O(n) steps of local computation (all the constants are small). The analysis of the algorithm involves approximating Markov chains by deterministic models.