# HG changeset patch
# User Madarasi Peter
# Date 1479933911 -3600
# Node ID a21760ed63d67771b2dd53891616db53110b15e7
# Parent  d35847f1417843e13743ec03c6041799362424be
Under 30

diff -r d35847f14178 -r a21760ed63d6 damecco.tex
--- a/damecco.tex	Wed Nov 23 21:15:26 2016 +0100
+++ b/damecco.tex	Wed Nov 23 21:45:11 2016 +0100
@@ -508,8 +508,9 @@
 
 
 \begin{algorithm}
-\algtext*{EndIf}%ne nyomtasson end if-et \algtext*{EndFor}%ne
-nyomtasson ..  \algtext*{EndProcedure}%ne nyomtasson ..
+\algtext*{EndIf}%ne nyomtasson end if-et
+\algtext*{EndFor}%ne
+\algtext*{EndProcedure}%ne nyomtasson ..
 \caption{\hspace{0.5cm}$A\ high\ level\ description\ of\ VF2$}\label{alg:VF2Pseu}
 \begin{algorithmic}[1]
 
@@ -866,6 +867,7 @@
 \algtext*{EndIf}
 \algtext*{EndProcedure}
 \algtext*{EndWhile}
+\algtext*{EndFor}
 \caption{\hspace{0.5cm}$The\ method\ of\ VF2++\ for\ determining\ the\ node\ order$}\label{alg:VF2PPPseu}
 \begin{algorithmic}[1]
 \Procedure{VF2++order}{} \State $\mathcal{M}$ := $\emptyset$
@@ -922,7 +924,7 @@
 \begin{claim}
 \[LabCut_{IND}((u,v),M(s))\!:=\!\!\!\!\!\bigvee_{l\ is\ label}\!\!\!\!\!\!\!|\Gamma_{large}^{l} (v) \cap T_{large}(s)|\!<\!|\Gamma_{small}^{l}(u)\cap T_{small}(s)|\ \vee\]\[\bigvee_{l\ is\ label} \newline |\Gamma_{large}^{l}(v)\cap \tilde{T}_{large}(s)| < |\Gamma_{small}^{l}(u)\cap \tilde{T}_{small}(s)|\] is a cutting function by IND.
 \end{claim}
-The following claims can be proven similarly.
+
 \subsubsection{Graph isomorphism}
 \begin{claim}
 \[LabCut_{ISO}((u,v),M(s))\!:=\!\!\!\!\!\bigvee_{l\ is\ label}\!\!\!\!\!\!\!|\Gamma_{large}^{l} (v) \cap T_{large}(s)|\!\neq\!|\Gamma_{small}^{l}(u)\cap T_{small}(s)|\  \vee\]\[\bigvee_{l\ is\ label} \newline |\Gamma_{large}^{l}(v)\cap \tilde{T}_{large}(s)| \neq |\Gamma_{small}^{l}(u)\cap \tilde{T}_{small}(s)|\] is a cutting function by ISO.
@@ -998,12 +1000,6 @@
 Representing $\mathcal{M}\subseteq V_{small}$ as an array of
 size $|V_{small}|$, both the computation of the BFS tree, and processing its levels by Algorithm~\ref{alg:VF2PPProcess1} can be done inplace by swapping nodes.
 
-After a node $u$ gets to the next place of the node order,
-$F_\mathcal{M}[lab[u]]$ has to be decreased by one, because there is
-one less covered node in $V_{large}$ with label $lab(u)$, that is why
-min selection sort is preferred which gives the elements from left to
-right in descending order, see Algorithm~\ref{alg:VF2PPProcess1}.
-
 \subsubsection{Cutting rules}
 In Section~\ref{VF2PPCuttingRules}, the cutting rules were
 described using the sets $T_{small}$, $T_{large}$, $\tilde T_{small}$