Acyclic orientations do not lead to optimal deadlock-free packet routing algorithms

In this paper we consider the problem of designing deadlock-free shortest-path routing algorithms. A design technique based on acyclic orientations has proven to be useful for many important topologies, e.g., meshes, tori, trees and hypercubes. It was not known whether this technique always leads to algorithms using an asymptotically optimal number of buffers. We show this is not the case by presenting a graph of sizeN which has a deadlock-free shortest-path routing algorithm using O(1) buffers, but every deadlock-free shortest-path routing algorithm based on acyclic orientations requires(logN / log logN ) buffers.  2000 Elsevier Science B.V. All rights reserved.