An Improved Randomized Selection Algorithm With an Experimental Study

A common statistical problem is that of nding the median element in a set of data. This paper presents an eÆcient randomized high-level parallel algorithm for nding the median given a set of elements distributed across a parallel machine. In fact, our algorithm solves the general selection problem that requires the determination of the element of rank k, for an arbitrarily given integer k. Our general framework is an SPMD distributed memory programming model that is en-hanced by a set of communication primitives. We use eÆcient techniques for distributing and coalescing data as well as eÆcient combinations of task and data parallelism. The algorithms have been coded in the message passing standard MPI, and our experimental results from the IBM SP-2 illustrate the scalability and eÆciency of our algorithm and improve upon all the related experimental results known to the authors