On the power of randomization for the common PRAM

Recent years have seen a dramatic increase in the number of nearly-constant time parallel algorithms. Paradigms and techniques have been developed to exploit the power of randomization and to obtain O(lg*n) time, linear work algorithms for quite a few problems, including linear approximate compaction, load balancing, approximate prefix sums, and range-minima. These algorithms run on most of the popular CRCW PRAM models which allow conflict in concurrent write. However, none of the newly-developed log-star algorithms run on the COMMON CRCW PRAM, one of the more studied CRCW models in the literature on parallel algorithms. The COMMON model requires processors writing simultaneously into the same memory cell to write the same value only. This restriction, which forbids conflicts in concurrent write, makes it difficult to claim resources at random - an operation which is at the heart of the fast randomized algorithms mentioned above-and it may have led to the belief that randomization has limited utility on the COMMON. In this paper we show that in many cases this inherent difficulty can be circumvented, and we present the first log-star COMMON algorithms for a number of fundamental problems. Thus, our results provide the first broad demonstration of the power of randomization for the COMMON model