On Implementing EREW Work-Optimally on Mesh of Trees

We show how to implement an `1 n log n-processor EREW PRAM workoptimally on a 2-dimensional n-sided mesh of trees, consisting of n processors, n memory modules, and O(n) nodes. Similarly, we prove that an `2 n log n-processor EREW PRAM can be implemented work-optimally on a 3-dimensional n-sided mesh of trees. By the work-optimality of implementations we mean that the expected routing time of PRAM memory requests is O(1) per simulated PRAM processor with high probability. Experiments show that on relatively small `1 and `2 the cost per simulated PRAM processor is 1:5{2:5 in the 2-dimensional case, and 2{3 in the 3-dimensional case. If at each step at most 1 3 'th of the PRAM processors make a reference to the shared memory, then the simulation cost is approximately 1. We also compare our work-optimal simulations to those proposed for coated meshes.