A Wait-Free Sorting Algorithm

Abstract

Sorting is one of a set of fundamental problems in computer science. In this paper we present the first wait-free algorithm for sorting an input array of size N using P ≤ N processors to achieve optimal running time. We show two variants of the algorithm, one deterministic and one randomized, and prove that, with high probability, the latter suffers no more than $O(\sqrt{P})$ contention when run synchronously. Known sorting algorithms, when made wait-free through previously established transformation techniques, have complexity O(log 3 N) . The algorithm we present here, when run in the CRCW PRAM model, executes with high probability in O(log N) time when P=N , and O((Nlog N)/P) otherwise, which is optimal amongst comparison-based sorting algorithms. The wait-free property guarantees that the sort will complete despite any delays or failures incurred by the processors. This is a very desirable property from an operating systems point of view, since it allows oblivious thread scheduling as well as thread creation and deletion, without fear of losing the algorithm's correctness.