From: Martin Mares <mj@ucw.cz>
Date: Fri, 1 Feb 2008 10:43:09 +0000 (+0100)
Subject: Named the Active Edge Jarnik's algorithm.
X-Git-Tag: printed~259
X-Git-Url: http://mj.ucw.cz/gitweb/?a=commitdiff_plain;h=42837849b8cc691427f7b2472a18245858750174;p=saga.git

Named the Active Edge Jarnik's algorithm.
---

diff --git a/adv.tex b/adv.tex
index e8c0fca..155bd98 100644
--- a/adv.tex
+++ b/adv.tex
@@ -194,7 +194,7 @@ active edge for~$w$ and replace it by~$vw$ if the new edge is lighter.
 The following algorithm shows how these operations translate to insertions, decreases
 and deletions on the heap.
 
-\algn{Jarn\'\i{}k with active edges; Fredman and Tarjan \cite{ft:fibonacci}}\id{jarniktwo}%
+\algn{Active Edge Jarn\'\i{}k; Fredman and Tarjan \cite{ft:fibonacci}}\id{jarniktwo}%
 \algo
 \algin A~graph~$G$ with an edge comparison oracle.
 \:$v_0\=$ an~arbitrary vertex of~$G$.
@@ -279,14 +279,14 @@ for sufficiently dense graphs. In some cases, it is useful to combine it with
 another MST algorithm, which identifies a~part of the MST edges and contracts
 the graph to increase its density. For example, we can perform several
 iterations of the Contractive Bor\o{u}vka's algorithm and find the rest of the
-MST by the Jarn\'\i{}k's algorithm.
+MST by the Active Edge Jarn\'\i{}k's algorithm.
 
 \algn{Mixed Bor\o{u}vka-Jarn\'\i{}k}
 \algo
 \algin A~graph~$G$ with an edge comparison oracle.
 \:Run $\log\log n$ iterations of the Contractive Bor\o{u}vka's algorithm (\ref{contbor}),
   getting a~MST~$T_1$.
-\:Run the Jarn\'\i{}k's algorithm with active edges (\ref{jarniktwo}) on the resulting
+\:Run the Active Edge Jarn\'\i{}k's algorithm (\ref{jarniktwo}) on the resulting
   graph, getting a~MST~$T_2$.
 \:Combine $T_1$ and~$T_2$ to~$T$ as in the Contraction lemma (\ref{contlemma}).
 \algout Minimum spanning tree~$T$.
@@ -305,7 +305,7 @@ and both trees can be combined in linear time, too.
 
 \para
 Actually, there is a~much better choice of the algorithms to combine: use the
-improved Jarn\'\i{}k's algorithm multiple times, each time stopping after a~while.
+Active Edge Jarn\'\i{}k's algorithm multiple times, each time stopping after a~while.
 A~good choice of the stopping condition is to place a~limit on the size of the heap.
 We start with an~arbitrary vertex, grow the tree as usually and once the heap gets too large,
 we conserve the current tree and start with a~different vertex and an~empty heap. When this
@@ -322,7 +322,7 @@ contract the graph along the edges of~this forest and iterate.
 \::$F\=\emptyset$. \cmt{forest built in the current phase}
 \::$t\=2^{\lceil 2m_0/n \rceil}$. \cmt{the limit on heap size}
 \::While there is a~vertex $v_0\not\in F$:
-\:::Run the improved Jarn\'\i{}k's algorithm (\ref{jarniktwo}) from~$v_0$, stop when:
+\:::Run the Active Edge Jarn\'\i{}k's algorithm (\ref{jarniktwo}) from~$v_0$, stop when:
 \::::all vertices have been processed, or
 \::::a~vertex of~$F$ has been added to the tree, or
 \::::the heap has grown to more than~$t$ elements.