Optimal simulations between mesh-connected arrays of processors

Let G and H be two mesh-connected arrays of processors, where G=glxg':!.X· .. xg, • H=h(x.h2x· .. Md.. and g 1· .. gr~ I" . hd. We consider the problem of simulating G by H. and we characterize in terms of the gi'S and h j ' s the best possible simulation by giving such a simulation and proving its optimality in the worst-case sense. We also establish the same bound on the average cost of encoding the edges of G as dis· tinCt paths in H .