Crossbar Based Model Provides Viable Platform for PRAM Simulation

The Parallel Random Access Machine or PRAM model, has been a much employed parallel algorithm development tool for a number of years. As such many important problems have been solved on this model. The purpose of this paper is to present non-trivial lower bounds for a linear array with reconfigurable global buses (LARGB), which is based on the cross-bar network. To achieve this goal we present efficient simulations of LARGB on the Concurrent-Read- Exclusive-Write Parallel Random Access Machine, CREW-PRAM and Concurrent-Read-Concurrent-Write PRAM, CRCW-PRAM. From this, known computational lower bounds for the PRAMs are transferred to the LARGB. Specifically, we show that any computation that takes O(t(n)) steps on an n-processor LARGB can be performed in O(t(n)) steps on an n- processor CREW-PRAM with O(n) extra memory. To the best of our knowledge these are the first non-trivial lower bounds obtained for the LARGB. Additionally, to the best of our knowledge, these are the first lower bounds to be presented for any cross-bar based model.