Parallel selection by regular sampling

Bulk-synchronous parallelism (BSP) is a simple and efficient paradigm for parallel algorithm design and analysis. In this paper, we present a new simple deterministic BSP algorithm for the classical problem of selecting the k-th smallest element from an array of size n, for a. given k, on a parallel computer with p processors. Our algorithm is based on the technique of regular sampling. It runs in optimal O(n/p) local computation and communication, and near-optimal O(log log p) synchronisation. The algorithm is of theoretical interest, as it gives an improvement in the asymptotic synchronisation cost over its predecessors. It is also simple enough to be implementable