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We study the power of shared-memory in models of parallel computation. We describe a novel distributed data structure that eliminates the need for shared mernory without significantly increasing the run time of the parallel computation. We also show how a complete network of processors can deterministicly simulate one PRAM step in O(log n(loglog n)2) time, when both models use n processors, and ttie size of the PRAM'S shared memory is polynomial in n. (The best previously known upper bound was the trivial O(n)). We also establish that this upper bound is nearly optimal. We prove that an online simulation of T PRAM steps by a complete network of processors requires Ω(Tlog n/loglog n) time.