Unifying themes for network selection

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 time O(n/p log log p + T ^s_p log n), where T ^s_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 T ^s_p ). As an example, our algorithm runs on a √p × √p mesh in time O(n/p log log p + √p log n), where n is the input size. This time bound is nearly optimal and significantly better than that of the best existing algorithm when n is large.

On the other hand, our randomized algorithm runs in an expected time of O((n/p + T ^s_sparse ) log log p) on any network, where T ^s_sparse is the time needed for collecting and sorting p ^1−ε sample keys using p processors. (Here ε is a constant < 1). On a √p × √p mesh our algorithm runs in an expected O((n/p + √p) log log p) time, a significant improvement over the deterministic algorithm.

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.

This research was supported in part by an NSF Research Initiation Award CCR-92-09260.