<s>
The	O
Kirkpatrick	B-Algorithm
–	I-Algorithm
Seidel	I-Algorithm
algorithm	I-Algorithm
,	O
proposed	O
by	O
its	O
authors	O
as	O
a	O
potential	O
"	O
ultimate	B-Algorithm
planar	I-Algorithm
convex	I-Algorithm
hull	I-Algorithm
algorithm	I-Algorithm
"	O
,	O
is	O
an	O
algorithm	O
for	O
computing	O
the	O
convex	O
hull	O
of	O
a	O
set	O
of	O
points	O
in	O
the	O
plane	O
,	O
with	O
time	B-General_Concept
complexity	I-General_Concept
,	O
where	O
is	O
the	O
number	O
of	O
input	O
points	O
and	O
is	O
the	O
number	O
of	O
points	O
(	O
non	O
dominated	O
or	O
maximal	O
points	O
,	O
as	O
called	O
in	O
some	O
texts	O
)	O
in	O
the	O
hull	O
.	O
</s>
<s>
Thus	O
,	O
the	O
algorithm	O
is	O
output-sensitive	B-Language
:	O
its	O
running	O
time	O
depends	O
on	O
both	O
the	O
input	O
size	O
and	O
the	O
output	O
size	O
.	O
</s>
<s>
Another	O
output-sensitive	B-Language
algorithm	I-Language
,	O
the	O
gift	B-Algorithm
wrapping	I-Algorithm
algorithm	I-Algorithm
,	O
was	O
known	O
much	O
earlier	O
,	O
but	O
the	O
Kirkpatrick	B-Algorithm
–	I-Algorithm
Seidel	I-Algorithm
algorithm	I-Algorithm
has	O
an	O
asymptotic	O
running	O
time	O
that	O
is	O
significantly	O
smaller	O
and	O
that	O
always	O
improves	O
on	O
the	O
bounds	O
of	O
non-output-sensitive	O
algorithms	O
.	O
</s>
<s>
The	O
Kirkpatrick	B-Algorithm
–	I-Algorithm
Seidel	I-Algorithm
algorithm	I-Algorithm
is	O
named	O
after	O
its	O
inventors	O
,	O
David	O
G	O
.	O
Kirkpatrick	O
and	O
Raimund	O
Seidel	O
.	O
</s>
<s>
The	O
basic	O
idea	O
of	O
the	O
algorithm	O
is	O
a	O
kind	O
of	O
reversal	O
of	O
the	O
divide-and-conquer	B-Algorithm
algorithm	I-Algorithm
for	O
convex	O
hulls	O
of	O
Preparata	O
and	O
Hong	O
,	O
dubbed	O
"	O
marriage-before-conquest	O
"	O
by	O
the	O
authors	O
.	O
</s>
<s>
The	O
traditional	O
divide-and-conquer	B-Algorithm
algorithm	I-Algorithm
splits	O
the	O
input	O
points	O
into	O
two	O
equal	O
parts	O
,	O
e.g.	O
,	O
by	O
a	O
vertical	O
line	O
,	O
recursively	O
finds	O
convex	O
hulls	O
for	O
the	O
left	O
and	O
right	O
subsets	O
of	O
the	O
input	O
,	O
and	O
then	O
merges	O
the	O
two	O
hulls	O
into	O
one	O
by	O
finding	O
the	O
"	O
bridge	O
edges	O
"	O
,	O
bitangents	O
that	O
connect	O
the	O
two	O
hulls	O
from	O
above	O
and	O
below	O
.	O
</s>
<s>
The	O
Kirkpatrick	B-Algorithm
–	I-Algorithm
Seidel	I-Algorithm
algorithm	I-Algorithm
splits	O
the	O
input	O
as	O
before	O
,	O
by	O
finding	O
the	O
median	O
of	O
the	O
x-coordinates	O
of	O
the	O
input	O
points	O
.	O
</s>
