On the network complexity of selection

The sequential complexity of determining the kth largest out of a given set of n keys is known to be linear. Thus, given a p-processor parallel machine, it is asked whether or not an O(n/p) selection algorithm can be devised for that machine. An Omega ((n/p) log log p+log p) lower bound is obtained for selection on any network that satisfies a particular low expansion property. The class of networks satisfying this property includes all of the common network families, such as the tree, multidimensional mesh, hypercube, butterfly, and shuffle-exchange. When n/p is sufficiently large (e.g. greater than log/sup 2/p on the butterfly, hypercube, and shuffle-exchange), this result is matched by the upper bound given previously by the author (Proc. 1st Ann. ACM Symp. on Parallel Algorithms and Architecture p.64-73, 1989).<
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