The Performance of Adaptive Routers on Worst Case Permutations

. Chaotic routing [4, 13, 14] is a randomized, nonminimal adaptive routing algorithm for multicomputers. An adaptive routing algorithm is one in which the path a packet takes from its source to its destination may depend on other packets it encounters. Such algorithms potentially avoid network bottlenecks by routing packets around "hot spots." Minimal adaptive routing algorithms have the additional advantage that the path each packet takes is a shortest one. Chinn, Leighton, and Tompa [6] provide a lower bound for permutation routing problems on the n \Theta n mesh for a large class of deterministic minimal adaptive algorithms. Specifically, they prove that for any such routing algorithm, there exists a permutation that requires\Omega (n 2 =k 2 ) steps to route all the packets in the permutation, where k is the number of packets a node can contain. We present experimental results showing the performance of the Chaos router on permutations for which a deterministic m..