document: There is no optimal routing policy for the torus A routing policy is the 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 J. Wu -LRB- 1996 -RRB- concerning an optimal routing policy for the torus
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