A new randomized sorting algorithm on the BSP model

We present a randomized algorithm for sorting n keys of any abstract data type on the p processors of a practical parallel computer model that is asymptotically optimal compared to the best available sequential sorting algorithm even when constant factors are taken into consideration. We designed and analyzed the performance of the algorithm in an architecture independent setting and expressed its running time and performance characteristics in terms of the problem size n and the parameters p, L and g of the Bulk-Synchronous Parallel model of computation. In particular, our new randomized sorting algorithm improves upon previously known BSP randomized sorting algorithms in the amount of parallel slackness required to achieve optimal speedup O(p), and the failure probability. Moreover, our methods are within a 1 + o(1) multiplicative factor of the corresponding sequential methods. While our methods are fairly simple themselves, the description of their performance in terms of the BSP parameters is somewhat complicated. The main reward for quantifying these complications, is that it enables software to be written once and for all that can be migrated efficiently among a variety of parallel machines.