Added a app for Sec 3 details

master
Atri Rudra 2020-12-13 21:53:22 -05:00
parent 82b682d92e
commit 4a52573012
3 changed files with 9 additions and 3 deletions

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hardness-app.tex Normal file
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\section{Missing details from Section~\ref{sec:hard}}
\label{app:hard}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% APPENDIX
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \clearpage
% \appendix
% \normalsize
\clearpage
\appendix
\normalsize
\input{hardness-app}
% \input{glossary.tex}
% \input{addproofappendix.tex}
\end{document}

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%root:main.tex
\section{Hardness of exact computation}
\label{sec:hard}
We would like to argue for a compressed version of $\poly(\vct{w})$, in general $\expct_{\vct{w}}\pbox{\poly(\vct{w})}$ even for TIDB, cannot be computed in linear time. We will argue two flavors of such a hardness result. In Section~\ref{sec:multiple-p}, we argue that computing the expected value exactly for all query polynommials $\poly(\vct{X})$ for multiple values of $p$ is \sharpwonehard. However, this does not rule out the possibility of being able to solve the problem for a any {\em fixed} value of $p$ being say even in linear time. In Section~\ref{sec:single-p}, we rule out even this possibility (based on some popular hardness conjectures in fine-grained complexity).