Better Deterministic Routing on Meshes

Optimal randomized and deterministic algorithms have been given for k-k routing on two-dimensional n n meshes. The deterministic algorithm is based on “column-sort” and exploits only part of the features of the mesh. For small n and moderate k, the lower-order terms of this algorithm make it considerably more expensive than the randomized algorithm. In this paper, we present a novel deterministic algorithm, which, by exploiting the topology of the mesh, has lowerorder terms that are almost negligible, even smaller than those of the randomized algorithm. An additional advantage of the new algorithm is that it routes average-case packet distributions twice as fast as worst-case distributions. In earlier algorithms this required additional steps for globally probing the distribution.