From 58e8ef5ba160d28e0d5757932987c7defa4fccbc Mon Sep 17 00:00:00 2001 From: Martin Mares Date: Sun, 4 May 2008 14:31:44 +0200 Subject: [PATCH] section -> Section (fix remaining). --- mst.tex | 2 +- ram.tex | 2 +- rank.tex | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/mst.tex b/mst.tex index 9729a06..5cccbb9 100644 --- a/mst.tex +++ b/mst.tex @@ -481,7 +481,7 @@ From this, we can conclude: The Jarn\'\i{}k's algorithm computes the MST of a~given graph in time $\O(m\log n)$. \rem -We will show several faster implementations in section \ref{iteralg}. +We will show several faster implementations in Section \ref{iteralg}. \paran{Kruskal's algorithm}% The last of the three classical algorithms processes the edges of the diff --git a/ram.tex b/ram.tex index c3fcf1f..bbf9cd9 100644 --- a/ram.tex +++ b/ram.tex @@ -1210,7 +1210,7 @@ Every operation on the Q-heap can be performed in a~constant number of vector operations and calculations of ranks. The ranks are computed in $\O(1)$ steps involving again $\O(1)$ vector operations, binary logarithms and bit extraction. All these can be calculated in constant -time using the results of section \ref{bitsect} and Lemma \ref{qhxtract}. +time using the results of Section \ref{bitsect} and Lemma \ref{qhxtract}. \qed \paran{Combining Q-heaps}% diff --git a/rank.tex b/rank.tex index b2c9421..8e4c202 100644 --- a/rank.tex +++ b/rank.tex @@ -580,7 +580,7 @@ use the Kasteleyn's algorithm \cite{kasteleyn:crystals} based on Pfaffian orientations which runs in time $\O(n^3)$. It has been recently extended to arbitrary surfaces by Yuster and Zwick \cite{yuster:matching} and sped up to $\O(n^{2.19})$. The counting problem -for arbitrary minor-closed classes (cf.~section \ref{minorclosed}) is still +for arbitrary minor-closed classes (cf.~Section \ref{minorclosed}) is still open. %-------------------------------------------------------------------------------- -- 2.39.2