<s>
In	O
computational	O
geometry	O
,	O
a	O
coreset	B-Algorithm
is	O
a	O
small	O
set	O
of	O
points	O
that	O
approximates	O
the	O
shape	O
of	O
a	O
larger	O
point	O
set	O
,	O
in	O
the	O
sense	O
that	O
applying	O
some	O
geometric	O
measure	O
to	O
the	O
two	O
sets	O
(	O
such	O
as	O
their	O
minimum	B-Algorithm
bounding	I-Algorithm
box	I-Algorithm
volume	O
)	O
results	O
in	O
approximately	O
equal	O
numbers	O
.	O
</s>
<s>
Many	O
natural	O
geometric	O
optimization	O
problems	O
have	O
coresets	B-Algorithm
that	O
approximate	O
an	O
optimal	O
solution	O
to	O
within	O
a	O
factor	O
of	O
,	O
that	O
can	O
be	O
found	O
quickly	O
(	O
in	O
linear	O
time	O
or	O
near-linear	O
time	O
)	O
,	O
and	O
that	O
have	O
size	O
bounded	O
by	O
a	O
function	O
of	O
independent	O
of	O
the	O
input	O
size	O
,	O
where	O
is	O
an	O
arbitrary	O
positive	O
number	O
.	O
</s>
<s>
When	O
this	O
is	O
the	O
case	O
,	O
one	O
obtains	O
a	O
linear-time	O
or	O
near-linear	O
time	O
approximation	O
scheme	O
,	O
based	O
on	O
the	O
idea	O
of	O
finding	O
a	O
coreset	B-Algorithm
and	O
then	O
applying	O
an	O
exact	O
optimization	O
algorithm	O
to	O
the	O
coreset	B-Algorithm
.	O
</s>
<s>
Regardless	O
of	O
how	O
slow	O
the	O
exact	O
optimization	O
algorithm	O
is	O
,	O
for	O
any	O
fixed	O
choice	O
of	O
,	O
the	O
running	O
time	O
of	O
this	O
approximation	O
scheme	O
will	O
be	O
plus	O
the	O
time	O
to	O
find	O
the	O
coreset	B-Algorithm
.	O
</s>
