Routing and sorting on mesh-connected arrays

Abstract

The problems of sorting and routing on n 1×... × n r mesh-connected arrays of processors are studied. A new sorting algorithm for r-dimensional meshes, r≥3, is presented. On meshes without wrap-around-connections it only needs 2(n 1+...+n r−1)+n r steps which is asymptotically optimal. For meshes with wrap-arounds the number of steps is asymptotically n 1+n 2+...+n r which is very close to the lower bound of (n 1+...+n r−1)+n r /2. Furthermore, for two-dimensional meshes a new deterministic routing algorithm is given for n×n meshes where each processor has a buffer of size f(n)<n. It needs 2n+O(n/f(n)) steps on meshes without wrap-arounds. Hence it is asymptotically optimal and as good as randomized algorithms routing data only with high probability.