A note on reducing parallel model simulations to integer sorting

We show that simulating a step of a FETCH&ADD PRAM model on an EREW PRAM model can be made as efficient as integer sorting. In particular, we present several efficient reductions of the simulation problem to various integer sorting problems. By using some recent algorithms for integer sorting, we get simulation algorithms on CREW and EREW that take o(n lg n) operations where n is the number of processors in the simulated CROW machine. Previous simulations were using Θ(n lg n) operations. Some of the more interesting simulation results are obtained by using a bootstrapping technique with a CRCW PRAM algorithm for hashing