Skip to content
GitLab
Menu
Projects
Groups
Snippets
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
Menu
Open sidebar
datovky
ds2-notes
Commits
e9ac7079
Commit
e9ac7079
authored
Aug 20, 2021
by
Ondřej Mička
Browse files
Graphs: Minor changes
parent
ae8844c7
Changes
1
Hide whitespace changes
Inline
Side-by-side
om-graphs/graphs.tex
View file @
e9ac7079
...
...
@@ -185,14 +185,13 @@ time.
\section
[linkcut]
{
Link-cut trees
}
Link-cut trees are dynamic version of the heavy-light decomposition. They allow us to
change structure of the represented forest by either linking two trees or by cutting an
edge inside a tree. Link-cut trees were introduced in a paper by Sleator and Tarjan
\TODO
reference
. However, we will show later version
that uses splay trees instead of original
biased binary trees
\TODO
reference
. Although it achieves the time complexity
only in amortized
case, it is significantly easier to analyze.
edge inside a tree. Link-cut trees were introduced in a paper by Sleator and Tarjan
in
1982
. However, we will show later version
from 1985, also by Sleator and Tarjan, that uses splay
trees instead of original
biased binary trees. Although it achieves the time complexity
only in amortized
case, it is significantly easier to analyze.
Link-cut tree represents a forest
$
F
$
of
\em
{
rooted
}
trees; each edge is oriented towards the
respective root. It supports following operations:
\TODO
proper formatting
\list
{
o
}
\:
Structural queries:
\tightlist
{
-
}
...
...
@@ -258,9 +257,8 @@ we jump to the top of the newly created fat path and repeat the whole process.
\figure
[expose-idea]
{
expose-idea.pdf
}{}{
One step of
$
\Expose
$
in the thin-fat
decomposition.
}
\theorem
{
\theorem
n
{
Sleator, Tarjan'82
}
{
$
\Expose
$
operation performs
$
\O
(
\log
n
)
$
steps amortized.
\TODO
reference S
\&
T'82
}
By using a balanced binary tree to represent fat paths, we obtain
...
...
Write
Preview
Supports
Markdown
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment