The queue-read queue-write asynchronous PRAM model

This paper presents results for the queue-read, queue-write asynchronous parallel random access machine (QRQW ASYNCHRONOUS PRAM) model, which is the asynchronous variant of the QRQW PRAM model. The QRQW PRAM family of models, which was introduced earlier by the authors, permit concurrent reading and writing to shared memory locations, but each memory location is viewed as having a queue which can service at most one request at a time In the basic QRQW PRAM model each processor executes a series of reads to shared memory locations, a series of local computation steps, and a series of writes to shared memory locations, and then synchronizes with all other processors; thus this can be viewed as a bulk-synchronous model. In contrast, in the QRQW ASYNCHRONOUS PRAM model discussed in this paper, there is no imposed bulk-synchronization between processors, and each processor proceeds at its own pace. Thus, the QRQW ASYNCHRONOUS PRAM serves as a better model for designing and analyzing truly asynchronous parallel algorithms than the original QRQW PRAM. In this paper we elaborate on the QRQW ASYNCHRONOUS PRAM model, and we demonstrate the power of asynchrony over bulk-synchrony by presenting a work and time optimal deterministic algorithm on the QRQW ASYNCHRONOUS PRAM for the leader election problem and a simple randomized work and time optimal algorithm on the QRQW ASYNCHRONOUS PRAM for sorting. In contrast, no tight bounds are known on the QRQW PRAM for either deterministic or randomized parallel algorithms for leader election and the only work and time optimal algorithms for sorting known on the QRQW PRAM are those inherited from the EREW PRAM, which are considerably more complicated. Our sorting algorithm is an asynchronous version of an earlier sorting algorithm we developed for the QRQW PRAM, for which we use an interesting analysis to bound the running time to be O(log n). We also present a randomized algorithm to simulate one step of a CRCW PRAM on a QRQW ASYNCHRONOUS PRAM in sublogarithmic time if the maximum contention in the step is relatively small.