<s>
A	O
kinetic	B-Data_Structure
diameter	I-Data_Structure
data	O
structure	O
is	O
a	O
kinetic	B-Data_Structure
data	I-Data_Structure
structure	I-Data_Structure
which	O
maintains	O
the	O
diameter	O
of	O
a	O
set	O
of	O
moving	O
points	O
.	O
</s>
<s>
In	O
the	O
two	O
dimensional	O
case	O
,	O
the	O
kinetic	B-Data_Structure
data	I-Data_Structure
structure	I-Data_Structure
for	O
kinetic	B-Algorithm
convex	I-Algorithm
hull	I-Algorithm
can	O
be	O
used	O
to	O
construct	O
a	O
kinetic	B-Data_Structure
data	I-Data_Structure
structure	I-Data_Structure
for	O
the	O
diameter	O
of	O
a	O
moving	O
point	O
set	O
that	O
is	O
responsive	O
,	O
compact	O
and	O
efficient	O
.	O
</s>
<s>
The	O
points	O
dualize	O
to	O
lines	O
and	O
the	O
convex	O
hull	O
of	O
the	O
points	O
dualizes	O
to	O
the	O
upper	B-Algorithm
and	I-Algorithm
lower	I-Algorithm
envelope	I-Algorithm
of	I-Algorithm
the	I-Algorithm
set	I-Algorithm
of	I-Algorithm
lines	I-Algorithm
.	O
</s>
<s>
The	O
vertices	O
of	O
the	O
upper	O
convex	O
hull	O
dualize	O
to	O
segments	O
on	O
the	O
upper	B-Algorithm
envelope	I-Algorithm
.	O
</s>
<s>
The	O
vertices	O
of	O
the	O
lower	O
convex	O
hull	O
dualize	O
to	O
segments	O
on	O
the	O
lower	B-Algorithm
envelope	I-Algorithm
.	O
</s>
<s>
When	O
viewed	O
in	O
this	O
dualized	O
fashion	O
the	O
antipodal	O
pairs	O
,	O
are	O
pairs	O
of	O
segments	O
,	O
one	O
from	O
the	O
upper	B-Algorithm
envelope	I-Algorithm
,	O
one	O
from	O
the	O
lower	O
,	O
with	O
overlapping	O
x	O
ranges	O
.	O
</s>
<s>
Now	O
,	O
the	O
upper	O
and	O
lower	B-Algorithm
envelopes	I-Algorithm
can	O
be	O
viewed	O
as	O
two	O
different	O
x-ordered	O
lists	O
of	O
non	O
overlapping	O
intervals	O
.	O
</s>
<s>
The	O
overlaps	O
in	O
the	O
merged	O
list	O
of	O
x-intervals	O
can	O
be	O
maintained	O
by	O
storing	O
the	O
endpoints	O
of	O
the	O
intervals	O
in	O
a	O
kinetic	B-Data_Structure
sorted	I-Data_Structure
list	I-Data_Structure
.	O
</s>
<s>
The	O
upper	O
and	O
lower	B-Algorithm
envelopes	I-Algorithm
can	O
be	O
maintained	O
using	O
the	O
standard	O
data	O
structure	O
for	O
kinetic	B-Algorithm
convex	I-Algorithm
hull	I-Algorithm
.	O
</s>
<s>
The	O
maximum	O
distance	O
between	O
pairs	O
of	O
antipodal	O
can	O
be	O
maintained	O
with	O
a	O
kinetic	B-Data_Structure
tournament	I-Data_Structure
.	O
</s>
<s>
Thus	O
,	O
using	O
kinetic	B-Algorithm
convex	I-Algorithm
hull	I-Algorithm
to	O
maintain	O
the	O
upper	O
and	O
lower	B-Algorithm
envelopes	I-Algorithm
,	O
a	O
kinetic	B-Data_Structure
sorted	I-Data_Structure
list	I-Data_Structure
on	O
these	O
intervals	O
to	O
maintain	O
the	O
antipodal	O
pairs	O
,	O
and	O
a	O
kinetic	B-Data_Structure
tournament	I-Data_Structure
to	O
maintain	O
the	O
pair	O
of	O
maximum	O
distance	O
apart	O
,	O
the	O
diameter	O
of	O
a	O
moving	O
point	O
set	O
can	O
be	O
maintained	O
.	O
</s>
<s>
The	O
data	O
structure	O
uses	O
space	O
because	O
the	O
kinetic	B-Algorithm
convex	I-Algorithm
hull	I-Algorithm
,	O
sorted	O
list	O
,	O
and	O
tournament	O
data	O
structures	O
all	O
use	O
space	O
.	O
</s>
<s>
This	O
data	O
structure	O
is	O
not	O
local	O
because	O
one	O
point	O
may	O
be	O
in	O
many	O
antipodal	O
pairs	O
,	O
and	O
thus	O
appear	O
many	O
times	O
in	O
the	O
kinetic	B-Data_Structure
tournament	I-Data_Structure
.	O
</s>
<s>
The	O
existence	O
of	O
a	O
local	O
kinetic	B-Data_Structure
data	I-Data_Structure
structure	I-Data_Structure
for	O
diameter	O
is	O
open	O
.	O
</s>
<s>
Efficiently	O
maintaining	O
the	O
kinetic	B-Data_Structure
diameter	I-Data_Structure
of	O
a	O
point	O
set	O
in	O
dimensions	O
higher	O
than	O
2	O
is	O
an	O
open	O
problem	O
.	O
</s>
<s>
Efficient	O
kinetic	B-Algorithm
convex	I-Algorithm
hull	I-Algorithm
in	O
dimensions	O
higher	O
than	O
2	O
is	O
also	O
an	O
open	O
problem	O
.	O
</s>
