Fundamental data movement algorithms for reconfigurable meshes

A number of data movement algorithms for the two-dimensional reconfigurable mesh are presented. These include computing the prefix sum of a binary sequence and computing the prefix maxima of a sequence of real numbers. These algorithms lead to a fast algorithm to sort a sequence of n reals in O(log n/log m) time on a reconfigurable mesh of size mn*n with 3<or=m<or=n. The result implies that sorting n real numbers takes O(1) time on a reconfigurable mesh of size n/sup 1.5/*n. The sorting algorithm uses significantly fewer processors than the best-known algorithm to date. Next, it is shown that computing the convex hull of a planar set of n points takes O(log n/log m) time on a reconfigurable mesh of size mn*n with 3<or=m<or=n. The result implies that the convex hull of n points in the plane can be coupled in O(1) time on a reconfigurable mesh of size n/sup 1.5/*n.<<ETX>>