From: Martin Mares <mj@ucw.cz>
Date: Wed, 9 Apr 2008 09:45:24 +0000 (+0200)
Subject: Remark on backtracking.
X-Git-Tag: printed~109
X-Git-Url: http://mj.ucw.cz/gitweb/?a=commitdiff_plain;h=65ee2b415a3f5cff3c77c38263c0f2d5d4a2ff53;p=saga.git

Remark on backtracking.
---

diff --git a/dyn.tex b/dyn.tex
index 502f618..279cfb3 100644
--- a/dyn.tex
+++ b/dyn.tex
@@ -168,10 +168,20 @@ Every \<Insert> performs $\O(1)$ operations on the Link-Cut forest, which take
 $\O(\log n)$ each by Theorem \ref{sletar}.
 \qed
 
+\rem
+We can easily extend the semidynamic MSF algorithm to allow an~operation commonly called
+\<Backtrack> --- removal of the most recently inserted edge. It is sufficient to keep the
+history of MSF changes in a~stack and reverse the most recent change upon backtrack.
+
+What are the obstacles to making the structure fully dynamic?
+Deletion of edges that do not belong to the MSF is trivial (we do not
+need to change anything) and so is deletion of bridges (we just remove the bridge
+from the Link-Cut tree, knowing that there is no edge to replace it). The hard part
+is the search for replacement edges after an~edge of the MSF is deleted.
 
 %--------------------------------------------------------------------------------
 
-\section{ET trees}
+\section{Eulerian Tour trees}
 
 
 \endpart