From: Martin Mares <mj@ucw.cz>
Date: Sat, 19 Apr 2008 12:30:43 +0000 (+0200)
Subject: Minor.
X-Git-Tag: printed~86
X-Git-Url: http://mj.ucw.cz/gitweb/?a=commitdiff_plain;h=7cb6494580b175ca7f258b2c06f84a41ba043e0b;p=saga.git

Minor.
---

diff --git a/adv.tex b/adv.tex
index 3b1e7ed..fe9ad19 100644
--- a/adv.tex
+++ b/adv.tex
@@ -312,7 +312,7 @@ and deletions on the heap.
 To analyze the time complexity of this algorithm, we will use the standard
 theorem on~complexity of the Fibonacci heap:
 
-\thmn{Fibonacci heaps} The~Fibonacci heap performs the following operations
+\thmn{Fibonacci heaps, Fredman and Tarjan \cite{ft:fibonacci}} The~Fibonacci heap performs the following operations
 with the indicated amortized time complexities:
 \itemize\ibull
 \:\<Insert> (insertion of a~new element) in $\O(1)$,
@@ -491,8 +491,8 @@ $$
 $$
 As soon as~$t_i\ge n$, the $i$-th phase must be final, because at that time
 there is enough space in the heap to process the whole graph. So~there are
-at most~$\beta(m,n)$ phases and we already know (Lemma~\ref{ijphase}) that each
-phase runs in linear time.
+at most~$\beta(m,n)$ phases and we already know that each phase runs in linear
+time (Lemma~\ref{ijphase}).
 \qed
 
 \cor