Abstract

This paper shows the power of randomization in designing efficient parallel algorithms for the problems of routing and PRAM emulation. We show that with randomization techniques optimal routing can be obtained for a large class of processor interconnection networks called leveled networks. This class includes well-known networks (e.g., mesh, hypercube and de Bruijn) as well as new ones (e.g., star graph, for which the network diameter is sub-logarithmic in the network size). Using the obtained routing algorithms, optimal emulations of the CROW PRAM on the leveled network and mesh are also given.

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