Fast, Efficient Mutual and Self Simulations for Shared Memory and Reconfigurable Mesh

This paper studies relations between the parallel random access machine (PRAM) model, and the recon-figurable mesh (RMESH) model, by providing mutual simulations between the models. We present an algorithm simulating one step of an (nlglgn)-processor CRCW PRAM on an n × n RMESH with delay O(lglgn) with high probability. We use our PRAM simulation to obtain the first efficient self-simulation algorithm of an RMESH with general switches: An algorithm running on an n × n RMESH is simulated on a p × p RMESH with delay O((n/p)2× lgn lglgp) with high probability, which is optimal for all p ≤ n/√lgnlglgn. Finally, we consider the simulation of RMESH on the PRAM. We show that a 2 × n RMESH can be optimally simulated on a CRCW PRAM in Θ(α(n)) time, where α(·) is the slow-growing inverse Ackermann function. In contrast, a PRAM with polynomial number of processors cannot simulate the 3 × n RMESH in less than Ω(lgn/lglgn) expected time.