From: Martin Mares <mj@ucw.cz>
Date: Sun, 6 Apr 2008 16:00:50 +0000 (+0200)
Subject: Use larger parens.
X-Git-Tag: printed~127
X-Git-Url: http://mj.ucw.cz/gitweb/?a=commitdiff_plain;h=0c48c9bcad405fbf12de3eade2cef5d73a37d23a;p=saga.git

Use larger parens.
---

diff --git a/opt.tex b/opt.tex
index 52934ce..9a3a76f 100644
--- a/opt.tex
+++ b/opt.tex
@@ -1036,7 +1036,7 @@ have exactly~$t$ vertices. We define the computation so that it labels the graph
 its optimal decision tree. Then we apply Theorem \ref{topothm} combined with the
 brute-force construction of optimal decision trees from Lemma \ref{odtconst}. Together they guarantee
 that we can assign the decision trees to the subgraphs in time:
-$$\O(\Vert\C\Vert + t^{t(2t+1)} \cdot (2^{2^{4t^2}} + t^2)) = \O(m).$$
+$$\O\Bigl(\Vert\C\Vert + t^{t(2t+1)} \cdot \bigl(2^{2^{4t^2}} + t^2\bigr)\Bigr) = \O(m).$$
 Execution of the decision tree on each subgraph~$C_i$ then takes $\O(D(C_i))$ steps.
 
 The contracted graph~$G_A$ has at most $n/t = \O(n / \log^{(3)}n)$ vertices and asymptotically