Efficiency of the Incomplete Enumeration algorithm for Monte-Carlo simulation of linear and branched polymers

Abstract

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 $n$ sites for large $n$ varies as $n^2$ for linear polymers, but as $exp(c n^α)$ for branched (undirected and directed) polymers, where $0<α<1$. On the binary tree, our numerical studies for $n$ of order $10^4$ gives $α= 0.333 \pm 0.005$. We argue that $α=1/3$ exactly in this case.