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 lower-order 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