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