Fast and Efficient Simulations among CRCW PRAMs

We study the problem of fast leaders election on TOLERANT, a CRCW PRAM model which tolerates concurrent write but does not support symmetry breaking. The leaders election problem is related to the problem of simulating stronger CRCW models, which support leaders election by predefined conflict resolution rules. We give a randomized simulation of MAXIMUM-a very strong CRCW PRAM-on TOLERANT. The simulation is optimal, is reliable, and runs in nearly doubly logarithmic time and linear space. This is the first simulation which is fast, optimal, and space-efficient, and therefore grants true comparison of algorithms running on different CRCW PRAMs. Moreover, it implies that the memory to which concurrent read or concurrent write is allowed should never be more than linear-the rest of the memory can always be addressed under the EREW convention. The techniques presented in this paper tackle fundamental difficulties in the design of fast parallel algorithms.

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