Sorting on the OTIS-mesh

In this paper we present sorting algorithms on the recently introduced N/sup 2/ processor OTIS-mesh, a network with diameter 4/spl radic/N-3 consisting of N connected meshes of size /spl radic/N/spl times//spl radic/N. We show that k-k sorting can be done in 8/spl radic/N+O(N/sup 1/3/) steps for k=1, 2, 3, 4 and in 2k/spl radic/N+O(kN/sup 1/3/) steps for k>4 with constant buffer-size for all k. We show how our algorithms can be modified to achieve 4/spl radic/N+O(N/sup 1/3/) steps for k=1, 2, 3, 4 and k/spl radic/N+O(kN/sup 1/3/) steps for k>4 in the average case. Finally, we show a lower bound of max{4/spl radic/N, 1//spl radic/2 k/spl radic/N} steps for k-k sorting.