An Optimal Shortest-Path Routing Policy for Network Computers with Regular Mesh-Connected Topologies
IEEE Transactions on Computers
The turn model for adaptive routing
ISCA '92 Proceedings of the 19th annual international symposium on Computer architecture
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
IEEE Transactions on Computers
Distance formula and shortest paths for the (n,k)-star graphs
Information Sciences: an International Journal
The number of shortest paths in the (n, k)-star graphs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
The number of shortest paths in the arrangement graph
Information Sciences: an International Journal
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method used to select a specific output channel for a message from among a number of acceptable output channels. An optimal routing policy is a policy that maximizes the probability of a message reaching its destination without delays. Optimal routing policies have been proposed for several regular networks, including the mesh and the hypercube. An open problem in interconnection network research has been the identification of an optimal routing policy for the torus. In this paper, we show that there is no optimal routing policy for the torus. Our result is demonstrated by presenting a detailed example in which the best choice of output channel is dependent on the probability of each channel being available. This result settles, in the negative, a conjecture by Wu concerning an optimal routing policy for the torus.