k-k Sorting on the Multi-Mesh

We present sorting algorithms on the recently introduced multi-mesh, a network consisting of n 2 meshes of size n n which are connected by the free marginal links of the meshes. Our algorithm takes 41n + o(n) steps which is a signiicant improvement to previously known algorithms. The sorting algorithm is based on a technique using interchange of data between the n n submeshes to distribute information uniformly, an approach which is similar to an all-to-all mapping. Furthermore , with this approach we can also handle k-k problems on the multi-mesh, where each processor contains k elements initially and nal-ly. We show that the k-k sorting problem can be solved in about 9:5kn steps, provided k 12.