Fast Routing on the Reconfigurable Meshmichael

We consider permutation routing problems on mesh connected processor arrays under a very weak model of reconnguration: we allow only uni-directional row or column buses, point-to-point communication, one-port-at-the-time serve by each processor. We present a scheme which is asympotically optimal for k-permutations, for any arbitrary k > 0. It works optimally on meshes of arbitrary dimensions d, from the linear array to hypercubic networks with d < n 1=3. We give an alternative scheme for 1-permutations, which is asymptotically slower, but with much better performance for realistic problem sizes.