Fast and feasible periodic sorting networks of constant depth

A periodic comparator network has depth (or period) k, if for every t>k, the compare-exchange operations performed at step t are executed between exactly the same registers as at step t-k. We introduce a general method that converts an arbitrary comparator network that sorts n items in time T(n) and that has layout area A into a periodic sorting network of depth 5 that sorts /spl Theta/(n/spl middot/T(n)) items in time O(T(n)/spl middot/log n) and has layout area O(A/spl middot/T(n)). This scheme applied to the AKS network yields a depth 5 periodic comparator network that sorts in time O(log/sup 2/ n). More practical networks with runtime O(log/sup 3/ n) can be obtained from Batcher's networks. Developing the techniques for the main result, we improve some previous results: Let us fix a d/spl isin/N. Then we can construct a network of depth 3 based on a d-dimensional mesh sorting n items in time O(n/sup 1/d//spl middot/log/sup O(d/) n).<
>