Selection on k-dimensional meshes with multiple broadcasting

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 shaw that we can find the p-ah 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 rasing an irregular N-(2k-1k+1/(k2k))x N-(2k-2k+1/(k2k)) x...x N-(k+1/(k2k)) 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 ai 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