Derandomizing algorithms for routing and sorting on meshes
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
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In this paper we introduce a new derandomization technique for mesh-connected arrays of processors that allows us to convert several recently proposed randomized algorithms for routing and sorting into deterministic algorithms that achieve the same running time, within a lower order additive term. By applying this technique, we obtain a number of optimal or improved deterministic algorithms for meshes and related networks. Among our main results are the first optimal deterministic algorithms for sorting on the two-dimensional mesh and for routing on the two-dimensional torus and the three-dimensional mesh, as well as an optimal deterministic routing algorithm for the two-dimensional mesh that achieves a queue size of 5. The new technique is very general and seems to apply to most of the randomized algorithms for routing and sorting on meshes and related networks that have been proposed so far.