<s>
In	O
information	B-Application
visualization	I-Application
and	O
computing	O
,	O
treemapping	B-Application
is	O
a	O
method	O
for	O
displaying	O
hierarchical	O
data	O
using	O
nested	B-General_Concept
figures	O
,	O
usually	O
rectangles	O
.	O
</s>
<s>
Treemaps	B-Application
display	O
hierarchical	O
(	O
tree-structured	B-Application
)	O
data	O
as	O
a	O
set	O
of	O
nested	B-General_Concept
rectangles	O
.	O
</s>
<s>
Often	O
the	O
leaf	B-Application
nodes	I-Application
are	O
colored	O
to	O
show	O
a	O
separate	O
dimension	O
of	O
the	O
data	O
.	O
</s>
<s>
A	O
second	O
advantage	O
of	O
treemaps	B-Application
is	O
that	O
,	O
by	O
construction	O
,	O
they	O
make	O
efficient	O
use	O
of	O
space	O
.	O
</s>
<s>
To	O
create	O
a	O
treemap	B-Application
,	O
one	O
must	O
define	O
a	O
tiling	B-Algorithm
algorithm	O
,	O
that	O
is	O
,	O
a	O
way	O
to	O
divide	O
a	O
region	O
into	O
sub-regions	O
of	O
specified	O
areas	O
.	O
</s>
<s>
Ideally	O
,	O
a	O
treemap	B-Application
algorithm	O
would	O
create	O
regions	O
that	O
satisfy	O
the	O
following	O
criteria	O
:	O
</s>
<s>
To	O
date	O
,	O
fifteen	O
primary	O
rectangular	O
treemap	B-Application
algorithms	O
have	O
been	O
developed	O
:	O
</s>
<s>
+	O
Treemap	B-Application
algorithms	O
Algorithm	O
Order	O
Aspect	O
ratios	O
Stability	O
BinaryTree	O
partially	O
orderedhigh	O
stable	O
Slice	O
And	O
Dice	O
orderedvery	O
high	O
stable	O
Strip	O
orderedmedium	O
medium	O
stability	O
Pivot	O
by	O
middle	O
orderedmedium	O
medium	O
stability	O
Pivot	O
by	O
split	O
orderedmedium	O
low	O
stability	O
Pivot	O
by	O
size	O
orderedmedium	O
medium	O
stability	O
Split	O
orderedmedium	O
medium	O
stability	O
Spiral	O
orderedmedium	O
medium	O
stability	O
Hilbert	O
orderedmedium	O
medium	O
stability	O
Moore	O
orderedmedium	O
medium	O
stability	O
Squarified	O
.	O
</s>
<s>
Rectangular	O
treemaps	B-Application
have	O
the	O
disadvantage	O
that	O
their	O
aspect	O
ratio	O
might	O
be	O
arbitrarily	O
high	O
in	O
the	O
worst	O
case	O
.	O
</s>
<s>
Convex	O
treemaps	B-Application
were	O
developed	O
in	O
several	O
steps	O
,	O
each	O
step	O
improved	O
the	O
upper	O
bound	O
on	O
the	O
aspect	O
ratio	O
.	O
</s>
<s>
In	O
convex	O
treemaps	B-Application
,	O
the	O
aspect	O
ratio	O
cannot	O
be	O
constant	O
-	O
it	O
grows	O
with	O
the	O
depth	O
of	O
the	O
tree	O
.	O
</s>
<s>
To	O
attain	O
a	O
constant	O
aspect-ratio	O
,	O
Orthoconvex	O
treemaps	B-Application
can	O
be	O
used	O
.	O
</s>
<s>
Voronoi	O
Treemaps	B-Application
based	O
on	O
Voronoi	B-Architecture
diagram	I-Architecture
calculations	O
.	O
</s>
<s>
Jigsaw	O
Treemaps	B-Application
based	O
on	O
the	O
geometry	O
of	O
space-filling	O
curves	O
.	O
</s>
<s>
GosperMaps	O
based	O
on	O
the	O
geometry	O
of	O
Gosper	B-Algorithm
curves	I-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
mosaic	B-Application
plots	I-Application
(	O
also	O
known	O
as	O
Marimekko	O
diagrams	O
)	O
use	O
rectangular	O
tilings	O
to	O
show	O
joint	O
distributions	O
(	O
i.e.	O
,	O
most	O
commonly	O
they	O
are	O
essentially	O
stacked	O
column	O
plots	O
where	O
the	O
columns	O
are	O
of	O
different	O
widths	O
)	O
.	O
</s>
<s>
The	O
main	O
distinguishing	O
feature	O
of	O
a	O
treemap	B-Application
,	O
however	O
,	O
is	O
the	O
recursive	O
construction	O
that	O
allows	O
it	O
to	O
be	O
extended	O
to	O
hierarchical	O
data	O
with	O
any	O
number	O
of	O
levels	O
.	O
</s>
<s>
Shneiderman	O
and	O
his	O
collaborators	O
then	O
deepened	O
the	O
idea	O
by	O
introducing	O
a	O
variety	O
of	O
interactive	O
techniques	O
for	O
filtering	O
and	O
adjusting	O
treemaps	B-Application
.	O
</s>
<s>
These	O
early	O
treemaps	B-Application
all	O
used	O
the	O
simple	O
"	O
slice-and-dice	O
"	O
tiling	B-Algorithm
algorithm	O
.	O
</s>
<s>
In	O
1999	O
Martin	O
Wattenberg	O
used	O
a	O
variation	O
of	O
the	O
"	O
squarifying	O
"	O
algorithm	O
that	O
he	O
called	O
"	O
pivot	O
and	O
slice	O
"	O
to	O
create	O
the	O
first	O
Web-based	O
treemap	B-Application
,	O
the	O
SmartMoney	O
Map	O
of	O
the	O
Market	O
,	O
which	O
displayed	O
data	O
on	O
hundreds	O
of	O
companies	O
in	O
the	O
U.S.	O
stock	O
market	O
.	O
</s>
<s>
Following	O
its	O
launch	O
,	O
treemaps	B-Application
enjoyed	O
a	O
surge	O
of	O
interest	O
,	O
especially	O
in	O
financial	O
contexts	O
.	O
</s>
<s>
A	O
third	O
wave	O
of	O
treemap	B-Application
innovation	O
came	O
around	O
2004	O
,	O
after	O
Marcos	O
Weskamp	O
created	O
the	O
Newsmap	O
,	O
a	O
treemap	B-Application
that	O
displayed	O
news	O
headlines	O
.	O
</s>
<s>
This	O
example	O
of	O
a	O
non-analytical	O
treemap	B-Application
inspired	O
many	O
imitators	O
,	O
and	O
introduced	O
treemaps	B-Application
to	O
a	O
new	O
,	O
broad	O
audience	O
.	O
</s>
<s>
In	O
recent	O
years	O
,	O
treemaps	B-Application
have	O
made	O
their	O
way	O
into	O
the	O
mainstream	O
media	O
,	O
including	O
usage	O
by	O
the	O
New	O
York	O
Times	O
.	O
</s>
