Optimal Tradeoffs Between Size and Slowdown for Universal Parallel Networks

Abstract

A parallel processor network is called n-universal with slowdown s if it can simulate each computation of each constant-degree processor network with n processors with slowdown s. We prove the following lower bound tradeoff: for each constant-degree n-universal network of size m with slowdown s, $m\cdot s=\Omega(n\log m)$ holds. Our tradeoff holds for a very general model of simulations. It covers all previously considered models and all known techniques for simulations among networks. For $m\ge n$ , this improves a previous lower bound by a factor of $\log\log n$ , proved for a weaker simulation model. For m < n, this is the first nontrivial lower bound for this problem. In this case this lower bound is asymptotically tight.