[For the entire collection see Zbl 0563.00018.] A probabilistic algorithm for checking set disjointness and performing set intersection of two sets stored at 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 elements, 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.