OPTIMAL MULTISELECTION IN HYPERCUBES

We study efficient parallel solutions to the problem of selecting r elements at specified ranks from a set of n arbitrary elements, known as multiselection, in a hypercube with p<n processors. We propose two parallel algorithms based on different approaches, where one requires processors to operate in the SIMD mode, and the other in the MIMD mode. Our SIMD algorithm runs in O(n ϵ min{r, log p}) time when p = n 1−r for any 0<ϵ<1, which is cost-optimal when r≥p. With the same number of processors, our MIMD algorithm runs in O(n ϵ logr) time and is cost-optimal for any values of r. Both algorithms are more efficient than straightforward solutions and that of direct simulation of the optimal EREW algorithm.