<s>
The	O
dynamic	B-Algorithm
convex	I-Algorithm
hull	I-Algorithm
problem	O
is	O
a	O
class	O
of	O
dynamic	B-General_Concept
problems	I-General_Concept
in	O
computational	O
geometry	O
.	O
</s>
<s>
It	O
should	O
be	O
distinguished	O
from	O
the	O
kinetic	B-Algorithm
convex	I-Algorithm
hull	I-Algorithm
,	O
which	O
studies	O
similar	O
problems	O
for	O
continuously	O
moving	O
points	O
.	O
</s>
<s>
Dynamic	B-Algorithm
convex	I-Algorithm
hull	I-Algorithm
problems	O
may	O
be	O
distinguished	O
by	O
the	O
types	O
of	O
the	O
input	O
data	O
and	O
the	O
allowed	O
types	O
of	O
modification	O
of	O
the	O
input	O
data	O
.	O
</s>
<s>
Therefore	O
,	O
if	O
the	O
convex	O
hull	O
is	O
required	O
to	O
be	O
reported	O
in	O
traditional	O
way	O
as	O
a	O
polygon	O
,	O
the	O
lower	O
bound	O
for	O
the	O
worst-case	O
computational	B-General_Concept
complexity	I-General_Concept
of	O
the	O
recomputation	O
of	O
the	O
convex	O
hull	O
is	O
,	O
since	O
this	O
time	O
is	O
required	O
for	O
a	O
mere	O
reporting	O
of	O
the	O
output	O
.	O
</s>
<s>
This	O
lower	O
bound	O
is	O
attainable	O
,	O
because	O
several	O
general-purpose	O
convex	O
hull	O
algorithms	O
run	O
in	O
linear	O
time	O
when	O
input	O
points	O
are	O
ordered	B-Algorithm
in	O
some	O
way	O
and	O
logarithmic-time	O
methods	O
for	O
dynamic	O
maintenance	O
of	O
ordered	B-Algorithm
data	O
are	O
well-known	O
.	O
</s>
<s>
The	O
selected	O
representation	O
of	O
the	O
convex	O
hull	O
may	O
influence	O
on	O
the	O
computational	B-General_Concept
complexity	I-General_Concept
of	O
further	O
operations	O
of	O
the	O
overall	O
algorithm	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
point	O
in	O
polygon	O
query	O
for	O
a	O
convex	O
polygon	O
represented	O
by	O
the	O
ordered	B-Algorithm
set	O
of	O
its	O
vertices	O
may	O
be	O
answered	O
in	O
logarithmic	O
time	O
,	O
which	O
would	O
be	O
impossible	O
for	O
convex	O
hulls	O
reported	O
by	O
the	O
set	O
of	O
it	O
vertices	O
without	O
any	O
additional	O
information	O
.	O
</s>
<s>
Therefore	O
,	O
some	O
research	O
of	O
dynamic	B-Algorithm
convex	I-Algorithm
hull	I-Algorithm
algorithms	O
involves	O
the	O
computational	B-General_Concept
complexity	I-General_Concept
of	O
various	O
geometric	O
search	O
problems	O
with	O
convex	O
hulls	O
stored	O
in	O
specific	O
kinds	O
of	O
data	O
structures	O
.	O
</s>
