We consider the permutation routing problem on two-dimensional n/spl times/n meshes. To be practical, a routing algorithm is required to ensure very small queue sizes Q, and very low running time T, not only asymptotically but particularly also for the practically important n up to 1000. With a technique inspired by a scheme of Kaklamanis/Krizanc/Rao, we obtain a near-optimal result: T=2/spl middot/n+/spl Oscr/(1) with Q=2. Although Q is very attractive now, the lower order terms in T make this algorithm highly impractical. Therefore we present simple schemes which are asymptotically slower, but have T/spl sime/3/spl middot/n for all n and Q between 2 and 8.
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