From 27c1d117c45622c462f11b648cab1c1d185263f4 Mon Sep 17 00:00:00 2001
From: Marcin Chrzanowski <mc370754@students.mimuw.edu.pl>
Date: Thu, 16 Dec 2021 17:04:19 +0100
Subject: Small improvement in introduction

---
 mgr.tex | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

(limited to 'mgr.tex')

diff --git a/mgr.tex b/mgr.tex
index 1e1eeb9..0066062 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -98,11 +98,11 @@ single tree and formula, varying the valuations we ask about, and thus allow a
 preprocessing step over the formula and tree. In this case, the above naive
 algorithm could be improved with Amarilli et al.'s \cite{amarilli2019} data
 structure that allows updates of the underlying tree.  Let $m$ be the size of a
-given question, i.e. $|W_1 \cup ... \cup W_k|$.  Amarilli's result allows us to
-preprocess the tree in linear time, label it with a choice of $W_1, \ldots, W_k$
-in time $O(m \log n)$, then answer model checking in constant time, thus greatly
-improving over the naive algorithm for questions that talk about a small number
-of vertices compared to the size of the whole tree.
+given question, i.e. $m = |W_1 \cup \ldots \cup W_k|$. Amarilli's result allows
+us to preprocess the tree in linear time, label it with a choice of $W_1,
+\ldots, W_k$ in time $O(m \log n)$, then answer model checking in constant time,
+thus greatly improving over the naive algorithm for questions that talk about a
+small number of vertices compared to the size of the whole tree.
 
 \section{Main result}
 
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