Routing, merging, and sorting on parallel models of computation
Journal of Computer and System Sciences
Oblivious routing with limited buffer capacity
Journal of Computer and System Sciences
Constant queue routing on a mesh
Journal of Parallel and Distributed Computing
A lower bound for permutation routing on two-dimensional bused meshes
Information Processing Letters
On multidimensional packet routing for meshes with buses
Journal of Parallel and Distributed Computing
Trade-offs between communication throughput and parallel time
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Two Packet Routing Algorithms on a Mesh-Connected Computer
IEEE Transactions on Parallel and Distributed Systems
Parallel sorting with limited bandwidth
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
Routing problems on the mesh of buses
Journal of Algorithms
Efficient Randomized Routing Algorithms on the Two-Dimensional Mesh of Buses
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
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An optimal \lceil 1.5N^{1/2} \rceil lower bound is shown for oblivious routing on the mesh of buses, a two-dimensional parallel model consisting of N^{1/2}\times N^{1/2} processors, N^{1/2} row and N^{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^{1/2} buses and each processor can access two different buses. Apparently the three-dimensional model provides more communication facilities, namely, including 3N^{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., \Omega(N^{2/3}) steps, which is another important result of this paper.