Deterministic coin tossing with applications to optimal parallel list ranking

The following problem is considered: given a linked list of length n, compute the distance from each element of the linked list to the end of the list. The problem has two standard deterministic algorithms: a linear time serial algorithm, and an O(log n) time parallel algorithm using n processors. We present new deterministic parallel algorithms for the problem. Our strongest results are (1) O(log n log* n) time using n/(log n log* n) processors (this algorithm achieves optimal speed-up); (2) O(log n) time using n log^(k)n/log n processors, for any fixed positive integer k. The algorithms apply a novel “random-like” deterministic technique. This technique provides for a fast and efficient breaking of an apparently symmetric situation in parallel and distributed computation.