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 n2 for linear polymers for large n, but as exp(cnα) for branched (undirected and directed) polymers, where 0<α<1. On the binary tree, our numerical studies for n of order 104 gives α = 0.333±0.005. We argue that α =1/3 exactly in this case.