Efficiency of the Incomplete Enumeration Algorithm for Monte-Carlo Simulation of Linear and Branched Polymers

We study the efficiency of the incomplete enumeration algorithm for linear and branched polymers. There is a qualitative difference in the efficiency in these two cases. The average time to generate an independent sample of configuration of polymer with n monomers varies as n(2) for linear polymers for large n, but as exp(cn(alpha)) for branched (undirected and directed) polymers, where 0<alpha<1. On the binary tree, our numerical studies for n of order 10(4) gives alpha = 0.333 +/- 0.005. We argue that alpha =1/3 exactly in this case.