Deterministic Simulations of PRAMs on Bounded Degree Networks

The problem of simulating a PRAM with $n$ processors and memory size $m \geq n$ on an $n$-node bounded degree network is considered. A scheme is presented which simulates an arbitrary PRAM step in $O ((\log n \log m)/\log \log n)$ time in the worst case on an expander-based network. By extending a previously established lower bound, it is shown that the proposed simulation is optimal whenever $\Omega (n^{1 + \epsilon}) \leq m \leq O(2^{(\log n)\alpha})$ for some $\epsilon greater than O$ and some $\alpha > O$