Unifying Themes for Selection on Any Network

Abstract

In this paper we present efficient deterministic and randomized algorithms for selection on any interconnection network when the number of input keys (n) is ≥ the number of processors (p). Our deterministic algorithm runs on any network in timeO(n/plog logp+Tpslogn), whereTpsis the time needed for sortingpkeys usingpprocessors. On the other hand, our randomized algorithm runs in an expected time ofO((n/p+Tpsparse) log logp) on any network, whereTpsparseis the time needed for collecting and sortingp1−ϵsample keys usingpprocessors. (Here ϵ is a constant <1). Application of the above algorithms on the mesh and the hypercube yields better results than known before. We have implemented our randomized algorithm on the Connection Machine CM2. Experimental results obtained are promising. In this paper we also report our implementation details.