Memory Organization Schemes for Large Shared Data: A Randomized Solution for Distributed Memory Machines

We address the problem of organizing a set T of shared data into the memory modules of a Distributed Memory Machine (DMM) in order to minimize memory access conflicts during read operations. In this paper we present a new randomized scheme that, with high probability, performs any set of r unrelated read operations on the shared data set T in O(log r + log log |T |) parallel time with no memory conflicts and using O(r) processors. The set T is distributed into m DMM memory modules where m is polynomial in r and logarithmic in T , and the overall size of the shared memory used by our scheme is not larger than (1 + 1/ log |T |)|T | (this means that there is “almost” no data replication). The memory organization scheme and most part of all the computations of our method do not depend on the read requests, so they can be performed once and for all during an off-line phase. This is a relevant improvement over the previous deterministic method recently given in [1] when “real-time” applications are considered.