A Top-down design of a parallel dictionary using skip lists

Abstract

We present a top down design of a parallel PRAM dictionary using skip lists. More precisely, we give algorithms to search, insert or delete k elements in a skip list of n elements, in parallel. The algorithms are simple and easy to implement on real machines. All of them are iterative. They can be implemented in the EREW PRAM model using k processors in expected time O(log n + log k). The probability that there is a significant deviation from the expected time decreases as O(n^{-2}) for the search algorithm and as O(n^{-2}+k^{-2}) for the insertion and deletion algorithms.