From: Martin Mares <mj@ucw.cz>
Date: Tue, 3 Jun 2008 09:57:17 +0000 (+0200)
Subject: Fixes to the abstract.
X-Git-Tag: phd-final~19
X-Git-Url: http://mj.ucw.cz/gitweb/?a=commitdiff_plain;h=d1e4a2cba275f14d25792727d92130c8cd65749d;p=saga.git

Fixes to the abstract.
---

diff --git a/abstract.tex b/abstract.tex
index 4574e20..4028ebe 100644
--- a/abstract.tex
+++ b/abstract.tex
@@ -826,7 +826,7 @@ resulting graph.
 \algin A~connected graph~$G$ with an~edge comparison oracle.
 \:If $G$ has no edges, return an~empty tree.
 \:$t\=\lfloor\log^{(3)} n\rfloor$. \cmt{the size of clusters}
-\:Call \<Partition> (\ref{partition}) on $G$ and $t$ with $\varepsilon=1/8$. It returns
+\:Call the partitioning procedure (\ref{partthm}) on $G$ and $t$ with $\varepsilon=1/8$. It returns
   a~collection~$\C=\{C_1,\ldots,C_k\}$ of clusters and a~set~$R^\C$ of corrupted edges.
 \:$F_i \= \mst(C_i)$ for all~$i$, obtained using optimal decision trees.
 \:$G_A \= (G / \bigcup_i C_i) \setminus R^\C$. \cmt{the contracted graph}
@@ -868,7 +868,7 @@ Using any of these results, we can prove an~Ackermannian upper bound on the
 optimal algorithm:
 
 \thm
-The time complexity of the Optimal algorithm is $\O(m\alpha(m,n))$.
+The time complexity of the Optimal algorithm is $\O(m\timesalpha(m,n))$.
 
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