From 9f6754399de8644e4297270ad8d782b291a085c8 Mon Sep 17 00:00:00 2001 From: Atri Rudra Date: Wed, 8 Jun 2022 02:48:58 +0000 Subject: [PATCH] Update on Overleaf. --- introduction.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/introduction.tex b/introduction.tex index a9a1dca..8f4bc69 100644 --- a/introduction.tex +++ b/introduction.tex @@ -242,7 +242,7 @@ We adopt the two-step intensional model of query evaluation used in set-\abbrPDB $; (ii) \termStepTwo (\abbrStepTwo): Given $\poly(\vct{X})$ for each tuple, compute a $(1\pm \eps)$-approximation $\expct_{\randWorld\sim\bpd}\pbox{\poly(\vct{\randWorld})}$. Let $\timeOf{\abbrStepOne}(\query,\tupset,\circuit)$ denote the runtime of \abbrStepOne when it outputs $\circuit$ (a representation of $\poly$ as an arithmetic circuit --- more on this representation in~\Cref{sec:expression-trees}). -Denote by $\timeOf{\abbrStepTwo}(\circuit, \epsilon)$ (recall $\circuit$ is the output of \abbrStepOne) the runtime of \abbrStepTwo (when $\poly$ is input as $\circuit$). Then to answer if we can compute a $(1\pm \eps)$-approximation to the expected multiplicity +Denote by $\timeOf{\abbrStepTwo}(\circuit, \epsilon)$ (recall $\circuit$ is the output of \abbrStepOne) the runtime of \abbrStepTwo (when $\poly$ is input as $\circuit$). Then to answer if we can compute a $(1\pm \eps)$-approximation to the expected multiplicity, it is enough to answer the following: %which we can leverage~\Cref{def:reduced-poly} and~\Cref{lem:tidb-reduce-poly} to address the next formal objective: \begin{Problem}[\abbrCTIDB linear time approximation]\label{prob:big-o-joint-steps}