Before revision:   We find that  load balance in a system of n nodes improves multiplicatively with d as long as d = o\left(\log(n)\right), and improves exponentially as soon as d = \Theta\left(\log(n)\right).
After revision:  We find that load balance in a system of n nodes improves multiplicatively with d as long as d = o\left(\log(n)\right), and improves exponentially once d = \Theta\left(\log(n)\right).