Fast E cient Mutual and Self Simulations for Shared Memory and Recon gurable Mesh

This paper studies relations between the parallel random access machine pram model and the recon gurable mesh rmesh model by providing mutual simulations between the models We present an algorithm simulating one step of an n lg lgn processor crcw pram on an n n rmesh with delay O lg lgn with high probability We use our pram simulation to obtain the rst e cient 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 lg n lg lg p with high probability which is optimal for all p n plg n lg lg n Finally we consider the simulation of rmesh on the pram We show that a n rmesh can be optimally simulated on a crcw pram in $ n time where is the slow growing inverse Ackermann function In contrast a pram with polynomial number of processors cannot simulate the n rmesh in less than lgn lg lgn expected time