<s>
A	O
kinetic	B-Data_Structure
smallest	I-Data_Structure
enclosing	I-Data_Structure
disk	I-Data_Structure
data	O
structure	O
is	O
a	O
kinetic	B-Data_Structure
data	I-Data_Structure
structure	I-Data_Structure
that	O
maintains	O
the	O
smallest	O
enclosing	O
disk	O
of	O
a	O
set	O
of	O
moving	O
points	O
.	O
</s>
<s>
In	O
2	O
dimensions	O
,	O
the	O
best	O
known	O
kinetic	B-Data_Structure
smallest	I-Data_Structure
enclosing	I-Data_Structure
disk	I-Data_Structure
data	O
structure	O
uses	O
the	O
farthest	O
point	O
delaunay	B-Algorithm
triangulation	I-Algorithm
of	O
the	O
point	O
set	O
to	O
maintain	O
the	O
smallest	O
enclosing	O
disk	O
.	O
</s>
<s>
The	O
farthest-point	O
Delaunay	B-Algorithm
triangulation	I-Algorithm
is	O
the	O
dual	O
of	O
the	O
farthest-point	O
Voronoi	O
diagram	O
.	O
</s>
<s>
It	O
is	O
known	O
that	O
if	O
the	O
farthest-point	O
delaunay	B-Algorithm
triangulation	I-Algorithm
of	O
a	O
point	O
set	O
contains	O
an	O
acute	O
triangle	O
,	O
the	O
circumcircle	O
of	O
this	O
triangle	O
is	O
the	O
smallest	O
enclosing	O
disk	O
.	O
</s>
<s>
Thus	O
,	O
by	O
maintaining	O
the	O
kinetic	B-Data_Structure
diameter	I-Data_Structure
of	O
the	O
point	O
set	O
,	O
the	O
farthest-point	O
delaunay	B-Algorithm
triangulation	I-Algorithm
,	O
and	O
whether	O
or	O
not	O
the	O
farthest-point	O
delaunay	B-Algorithm
triangulation	I-Algorithm
has	O
an	O
acute	O
triangle	O
,	O
the	O
smallest	O
enclosing	O
disk	O
can	O
be	O
maintained	O
.	O
</s>
<s>
The	O
existence	O
of	O
kinetic	B-Data_Structure
data	I-Data_Structure
structure	I-Data_Structure
that	O
has	O
events	O
is	O
an	O
open	O
problem	O
.	O
</s>
<s>
The	O
smallest	O
enclosing	O
disk	O
of	O
a	O
set	O
of	O
n	O
moving	O
points	O
can	O
be	O
ε-approximated	O
by	O
a	O
kinetic	B-Data_Structure
data	I-Data_Structure
structure	I-Data_Structure
that	O
processes	O
events	O
and	O
requires	O
time	O
total	O
.	O
</s>
