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 $exp(c{n}^{\hat{I}}\pm )$ for branched (undirected and directed) polymers, where $0<\hat{I}\pm <1$. On the binary tree, our numerical studies for $n$ of order $10^4$ gives $\hat{I}\pm =0.333\pm 0.005$. We argue that $\hat{I}\pm =1/3$ exactly in this case.

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