How to share memory in a distributed system

The power of shared-memory in models of parallel computation is studied, and a novel distributed data structure that eliminates the need for shared memory without significantly increasing the run time of the parallel computation is described. More specifically, it is shown how a complete network of processors can deterministically simulate one PRAM step in <italic>O</italic>(log <italic>n</italic>/(log log <italic>n</italic>)<supscrpt>2</supscrpt>) time when both models use <italic>n</italic> processors and the size of the PRAM's shared memory is polynomial in <italic>n</italic>. (The best previously known upper bound was the trivial <italic>O</italic>(<italic>n</italic>)). It is established that this upper bound is nearly optimal, and it is proved that an on-line simulation of <italic>T</italic> PRAM steps by a complete network of processors requires &OHgr;(<italic>T</italic>(log <italic>n/</italic> log log <italic>n</italic>)) time. A simple consequence of the upper bound is that an Ultracomputer (the currently feasible general-purpose parallel machine) can simulate one step of a PRAM (the most convenient parallel model to program) in <italic>O</italic>((log <italic>n</italic>)<supscrpt>2</supscrpt>log log <italic>n</italic>) steps.