Oblivious routing algorithms on the mesh of buses

Abstract

An optimal [1.5N/sup 1/2/] lower bound is shown for oblivious routing on the mesh of buses, a two-dimensional parallel model consisting of N/sup 1/2//spl times/N/sup 1/2/ processors, N/sup 1/2/ row and N/sup 1/2/ column buses but no local connections between neighbouring processors. Many lower bound proofs for routing on mesh-structured models use a single instance (adversary) which includes difficult packet-movement. This approach does not work in our case; our proof is the first which exploits the fact that the routing algorithm has to cope with many different instances. Note that the two-dimensional mesh of buses includes 2N/sup 1/2/ buses and each processor can access two different buses. Apparently the three-dimensional model provides more communication facilities, namely, including 3N/sup 2/3/ buses and each processor can access three different buses. Surprisingly, however, the oblivious routing on the three-dimensional mesh of buses needs more time, i.e., /spl Omega/(N/sup 2/3/) steps, which is another important result of this paper.