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Abstract

Optimal randomized and deterministic algorithms have been given for $k$-$k$ routing on two-dimensional $n \times n$ 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.