ODIn/paper-BagRelationalPDBsAreHard
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Merge branch 'master' of gitlab.odin.cse.buffalo.edu:ahuber/SketchingWorlds

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Boris Glavic 2020-12-20 15:08:42 -06:00
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approx_alg.tex
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@ -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.