<s>
In	O
computational	O
geometry	O
,	O
the	O
largest	B-Algorithm
empty	I-Algorithm
rectangle	I-Algorithm
problem	O
,	O
maximal	B-Algorithm
empty	I-Algorithm
rectangle	I-Algorithm
problem	O
or	O
maximum	B-Algorithm
empty	I-Algorithm
rectangle	I-Algorithm
problem	O
,	O
is	O
the	O
problem	O
of	O
finding	O
a	O
rectangle	O
of	O
maximal	O
size	O
to	O
be	O
placed	O
among	O
obstacles	O
in	O
the	O
plane	O
.	O
</s>
<s>
A	O
maximal	B-Algorithm
empty	I-Algorithm
rectangle	I-Algorithm
is	O
a	O
rectangle	O
which	O
is	O
not	O
contained	O
in	O
another	O
empty	O
rectangle	O
.	O
</s>
<s>
Each	O
side	O
of	O
a	O
maximal	B-Algorithm
empty	I-Algorithm
rectangle	I-Algorithm
abuts	O
an	O
obstacle	O
(	O
otherwise	O
the	O
side	O
may	O
be	O
shifted	O
outwards	O
,	O
increasing	O
the	O
empty	O
rectangle	O
)	O
.	O
</s>
<s>
An	O
application	O
of	O
this	O
kind	O
is	O
enumeration	O
of	O
"	O
maximal	O
white	O
rectangles	O
"	O
in	O
image	B-Algorithm
segmentation	I-Algorithm
R&D	O
of	O
image	B-Algorithm
processing	I-Algorithm
and	O
pattern	O
recognition	O
.	O
</s>
<s>
In	O
the	O
contexts	O
of	O
many	O
algorithms	O
for	O
largest	B-Algorithm
empty	I-Algorithm
rectangles	I-Algorithm
,	O
"	O
maximal	B-Algorithm
empty	I-Algorithm
rectangles	I-Algorithm
"	O
are	O
candidate	O
solutions	O
to	O
be	O
considered	O
by	O
the	O
algorithm	O
,	O
since	O
it	O
is	O
easily	O
proven	O
that	O
,	O
e.g.	O
,	O
a	O
maximum-area	O
empty	O
rectangle	O
is	O
a	O
maximal	B-Algorithm
empty	I-Algorithm
rectangle	I-Algorithm
.	O
</s>
<s>
The	O
case	O
when	O
the	O
sought	O
rectangle	O
is	O
an	O
axis-oriented	O
square	O
may	O
be	O
treated	O
using	O
Voronoi	B-Architecture
diagrams	I-Architecture
in	O
metrics	O
for	O
the	O
corresponding	O
obstacle	O
set	O
,	O
similarly	O
to	O
the	O
largest	B-Algorithm
empty	I-Algorithm
circle	I-Algorithm
problem	O
.	O
</s>
<s>
Naamad	O
,	O
Lee	O
and	O
Hsu	O
presented	O
an	O
algorithm	O
of	O
time	O
complexity	O
,	O
where	O
s	O
is	O
the	O
number	O
of	O
feasible	O
solutions	O
,	O
i.e.	O
,	O
maximal	B-Algorithm
empty	I-Algorithm
rectangles	I-Algorithm
.	O
</s>
<s>
In	O
3-dimensional	O
space	O
,	O
algorithms	O
are	O
known	O
for	O
finding	O
a	O
largest	O
maximal	O
empty	O
isothetic	O
cuboid	B-General_Concept
problem	O
,	O
as	O
well	O
as	O
for	O
enumeration	O
of	O
all	O
maximal	O
isothetic	O
empty	O
cuboids	B-General_Concept
.	O
</s>
