<s>
A	O
Kinetic	B-Application
Priority	I-Application
Queue	I-Application
is	O
an	O
abstract	O
kinetic	B-Data_Structure
data	I-Data_Structure
structure	I-Data_Structure
.	O
</s>
<s>
It	O
is	O
a	O
variant	O
of	O
a	O
priority	B-Application
queue	I-Application
designed	O
to	O
maintain	O
the	O
maximum	O
(	O
or	O
minimum	O
)	O
priority	O
element	O
(	O
key-value	O
pair	O
)	O
when	O
the	O
priority	O
of	O
every	O
element	O
is	O
changing	O
as	O
a	O
continuous	O
function	O
of	O
time	O
.	O
</s>
<s>
Kinetic	B-Application
priority	I-Application
queues	I-Application
have	O
been	O
used	O
as	O
components	O
of	O
several	O
kinetic	B-Data_Structure
data	I-Data_Structure
structures	I-Data_Structure
,	O
as	O
well	O
as	O
to	O
solve	O
some	O
important	O
non-kinetic	O
problems	O
such	O
as	O
the	O
k-set	O
problem	O
and	O
the	O
connected	O
red	O
blue	O
segments	O
intersection	O
problem	O
.	O
</s>
<s>
There	O
are	O
several	O
variants	O
of	O
kinetic	B-Application
priority	I-Application
queues	I-Application
,	O
which	O
support	O
the	O
same	O
basic	O
operations	O
but	O
have	O
different	O
performance	O
guarantees	O
.	O
</s>
<s>
Some	O
of	O
the	O
most	O
common	O
implementations	O
are	O
kinetic	B-Application
heaps	I-Application
which	O
are	O
simple	O
to	O
implement	O
but	O
do	O
n't	O
have	O
tight	O
theoretical	O
performance	O
bounds	O
,	O
and	O
their	O
randomized	O
variants	O
-	O
kinetic	B-Application
heaters	I-Application
and	O
kinetic	B-Application
hangers	I-Application
-	O
which	O
are	O
easier	O
to	O
analyze	O
.	O
</s>
<s>
There	O
is	O
also	O
a	O
heap-like	O
structure	O
based	O
on	O
the	O
dynamic	B-Algorithm
convex	I-Algorithm
hull	I-Algorithm
data	O
structure	O
which	O
achieves	O
better	O
performance	O
for	O
affine	O
motion	O
of	O
the	O
priorities	O
,	O
but	O
does	O
n't	O
support	O
curved	O
trajectories	O
.	O
</s>
<s>
The	O
kinetic	B-Data_Structure
tournament	I-Data_Structure
is	O
another	O
commonly	O
used	O
implementation	O
.	O
</s>
<s>
Here	O
,	O
denotes	O
the	O
inverse	O
Ackermann	O
function.-intersecting	O
curves	O
refer	O
to	O
curves	O
where	O
each	O
pair	O
has	O
at	O
most	O
intersections	O
,	O
and	O
refers	O
to	O
a	O
term	O
in	O
the	O
Davenport-Schinzel	O
sequence	O
,	O
which	O
gives	O
the	O
maximum	O
size	O
of	O
the	O
upper	B-Algorithm
envelope	I-Algorithm
of	O
intersecting	O
curves	O
.	O
</s>
<s>
Kinetic	B-Application
priority	I-Application
queues	I-Application
are	O
used	O
as	O
part	O
of	O
other	O
kinetic	O
data	O
structures/algorithms	O
such	O
as	O
kinetic	B-Data_Structure
closest	I-Data_Structure
pair	I-Data_Structure
,	O
kinetic	O
max-cut	O
or	O
kinetic	O
clustering	O
.	O
</s>
