<s>
A	O
Kinetic	B-Application
Heater	I-Application
is	O
a	O
kinetic	B-Application
priority	I-Application
queue	I-Application
similar	O
to	O
a	O
kinetic	B-Application
heap	I-Application
,	O
that	O
makes	O
use	O
of	O
randomization	O
to	O
simplify	O
its	O
analysis	O
in	O
a	O
way	O
similar	O
to	O
a	O
treap	B-Application
.	O
</s>
<s>
Specifically	O
,	O
each	O
element	O
has	O
a	O
random	O
key	O
associated	O
with	O
it	O
in	O
addition	O
to	O
its	O
priority	O
(	O
which	O
changes	O
as	O
a	O
continuous	O
function	O
of	O
time	O
as	O
in	O
all	O
kinetic	B-Data_Structure
data	I-Data_Structure
structures	I-Data_Structure
)	O
.	O
</s>
<s>
The	O
kinetic	B-Application
heater	I-Application
is	O
then	O
simultaneously	O
a	O
binary	B-Language
search	I-Language
tree	I-Language
on	O
the	O
element	O
keys	O
,	O
and	O
a	O
heap	B-Application
on	O
the	O
element	O
priorities	O
.	O
</s>
<s>
The	O
kinetic	B-Application
heater	I-Application
achieves	O
(	O
expected	O
)	O
asymptotic	O
performance	O
bounds	O
equal	O
to	O
the	O
best	O
kinetic	B-Application
priority	I-Application
queues	I-Application
.	O
</s>
<s>
If	O
every	O
element	O
has	O
a	O
key	O
and	O
a	O
priority	O
associated	O
with	O
it	O
,	O
then	O
there	O
is	O
a	O
unique	O
tree	O
structure	O
that	O
is	O
simultaneously	O
a	O
search	O
tree	O
on	O
the	O
keys	O
and	O
a	O
heap	B-Application
on	O
the	O
priorities	O
-	O
this	O
structure	O
corresponds	O
to	O
the	O
treap	B-Application
(	O
if	O
the	O
priorities	O
are	O
randomly	O
chosen	O
)	O
or	O
the	O
kinetic	B-Application
heater	I-Application
(	O
if	O
the	O
keys	O
are	O
randomly	O
chosen	O
)	O
.	O
</s>
<s>
The	O
validity	O
of	O
the	O
tree	O
structure	O
is	O
ensured	O
by	O
creating	O
a	O
certificate	O
at	O
each	O
edge	O
that	O
enforces	O
the	O
heap	B-Application
property	I-Application
on	O
that	O
edge	O
.	O
</s>
<s>
The	O
main	O
operational	O
difference	O
between	O
a	O
kinetic	B-Application
heap	I-Application
and	O
a	O
kinetic	B-Application
heater	I-Application
is	O
in	O
how	O
they	O
respond	O
to	O
certificate	O
failures	O
.	O
</s>
<s>
When	O
a	O
certificate	O
on	O
an	O
edge	O
fails	O
,	O
a	O
kinetic	B-Application
heater	I-Application
will	O
perform	O
a	O
rotation	O
around	O
the	O
nodes	O
that	O
failed	O
(	O
instead	O
of	O
the	O
swap	O
that	O
a	O
kinetic	B-Application
heap	I-Application
would	O
perform	O
)	O
.	O
</s>
<s>
When	O
the	O
certificate	O
 [ B>D ] 	O
on	O
the	O
edge	O
BD	O
fails	O
,	O
the	O
tree	O
will	O
be	O
rotated	B-Data_Structure
around	O
this	O
edge	O
.	O
</s>
<s>
This	O
kinetic	B-Data_Structure
data	I-Data_Structure
structure	I-Data_Structure
is	O
:	O
</s>
<s>
Efficient	O
:	O
It	O
has	O
the	O
same	O
(	O
expected	O
)	O
asymptotic	O
performance	O
as	O
kinetic	B-Application
hanger	I-Application
,	O
kinetic	B-Data_Structure
tournament	I-Data_Structure
-	O
for	O
a	O
collection	O
of	O
space-time	O
trajectories	O
where	O
each	O
pair	O
intersects	O
at	O
most	O
times	O
,	O
the	O
kinetic	B-Application
heater	I-Application
processes	O
events	O
in	O
time	O
,	O
where	O
is	O
a	O
Davenport-Schinzel	O
sequence	O
.	O
</s>
