Deterministic Selection on the Mesh and Hypercube

In this paper we present efficient deterministic algorithms for selection on the mesh connected computers (referred to as the mesh from hereon) and the hypercube. Our algorithm on the mesh runs in time O([n/p] log logp + √p logn) where n is the input size and p is the number of processors. The time bound is significantly better than that of the best existing algorithms when n is large. The run time of our algorithm on the hypercube is O ([n/p] log log p + Ts/p log nM/em>), where Ts/p is the time needed to sort p element on a p-node hypercube. In fact, the same algorithm runs on an network in time O([n/p] log log p +Ts/p log), where Ts/p is the time needed for sorting p keys using p processors (assuming that broadcast and prefix computations take time less than or equal to Ts/p.