Randomized Routing and PRAM Emulation on Parallel Machines

This paper shows the power of randomization in designing e cient 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 CRCW PRAM on the leveled network and mesh are also given.