From 6f3fb7798e9b1cf02d94f114345bc750addacad7 Mon Sep 17 00:00:00 2001 From: Aaron Huber Date: Sun, 20 Dec 2020 16:00:50 -0500 Subject: [PATCH] Small fix on S4 macro not called --- approx_alg.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/approx_alg.tex b/approx_alg.tex index 8f7b387..9a77cca 100644 --- a/approx_alg.tex +++ b/approx_alg.tex @@ -412,7 +412,7 @@ It turns out that for proof of~\Cref{lem:sample}, we need to argue that when $\e %Algorithm ~\ref{alg:sample} takes $\etree$ as input, samples an arbitrary $(\monom, \coef)$ from $\expandtree{\etree}$ with probabilities $\stree_\lchild.\wght$ and $\stree_\rchild.\wght$ for each subtree $\stree$ with $\stree.\type = +$, outputting the tuple $(\monom, \sign(\coef))$. While one cannot compute $\expandtree{\etree}$ in time better than $O(N^k)$, the algorithm, similar to \textsc{OnePass}, uses a technique on $\etree$ which produces a sample from $\expandtree{\etree}$ without ever materializing $\expandtree{\etree}$. -A naive (slow) implementation of \sampmon\ would first compute $E(T)$ and then sample from it. +A naive (slow) implementation of \sampmon\ would first compute $\expandtree{\etree}$ and then sample from it. % However, this would be too time consuming. % Instead, \Cref{alg:sample} selects a monomial from $\expandtree{\etree}$ by top-down traversal.