Selection on k-Dimensional Meshes with Multiple Broadcasting

Abstract

Randomized selection algorithms on k-dimensional mesh-connected computers with multiple broadcasting are proposed in this paper. We first show that a leader can be elected in O(log N) time on any k-dimensional mesh-connected computers with multiple broadcasting of size N. We then show that we can find the p-th smallest element among a data set of size N in O((log N + k + N 1/(k(k+1)) ) log N) expected time using a regular N 1/k x... x N 1/k k-dimensional mesh and in O((log N + k 2 N 1/(k2k) )log N) expected time using an irregular N (2k-1k+1)/(k2k) x N (2k-2k+1)/(k2k) x... x N (k+1)/(k2k) k-dimensional mesh. This leads to a selection algorithm which runs in O((log N) 2 ) expected time on a regular ((log N/log log N) 1/2 )-dimensional mesh or on an irregular (log log N)-dimensional mesh each with N processors. To our best knowledge, this is the first polylogarithmic selection algorithm on meshes with multiple broadcasting.