The Log-Star Revolution

The last approximately one year has witnessed a dramatic change in the way theoreticians think about computing on the randomized concurrent-read concurrent-write parallel random access machine (CRCW PRAM). Today we have superfast algorithms that were inconceivable a few years ago. Many of these having running times of the form O((log*n)c), for some small constant c e N, the name “log-star revolution” seems appropriate. This paper tries to put some of the most important results obtained next to each other and to explain their significance. In order to keep the exposition properly focussed, we restrict our attention to problems of a very fundamental nature that, in an ideal environment, would be handled by the operating system of a parallel machine rather than by each applications programmer: Processor allocation, memory allocation and the implementation of a particular conflict resolution rule for concurrent writing. The main contention of the paper is that the theoretical groundwork for providing such an ideal environment has been laid.