<s>
A	O
Kinetic	B-Data_Structure
Tournament	I-Data_Structure
is	O
a	O
kinetic	B-Data_Structure
data	I-Data_Structure
structure	I-Data_Structure
that	O
functions	O
as	O
a	O
priority	B-Application
queue	I-Application
for	O
elements	O
whose	O
priorities	O
change	O
as	O
a	O
continuous	O
function	O
of	O
time	O
.	O
</s>
<s>
It	O
supports	O
the	O
usual	O
priority	B-Application
queue	I-Application
operations	O
-	O
insert	O
,	O
delete	O
and	O
find-max	O
.	O
</s>
<s>
They	O
are	O
often	O
used	O
as	O
components	O
of	O
other	O
kinetic	B-Data_Structure
data	I-Data_Structure
structures	I-Data_Structure
,	O
such	O
as	O
kinetic	B-Data_Structure
closest	I-Data_Structure
pair	I-Data_Structure
.	O
</s>
<s>
A	O
kinetic	B-Data_Structure
tournament	I-Data_Structure
is	O
organized	O
in	O
a	O
binary	O
tree-like	O
structure	O
,	O
where	O
the	O
leaves	O
contain	O
the	O
elements	O
,	O
and	O
each	O
internal	O
node	O
contains	O
the	O
larger	O
(	O
or	O
smaller	O
)	O
of	O
the	O
elements	O
in	O
its	O
child	B-Data_Structure
nodes	I-Data_Structure
.	O
</s>
<s>
Thus	O
,	O
the	O
root	B-Application
of	O
the	O
tree	O
contains	O
the	O
maximum	O
(	O
or	O
minimum	O
)	O
element	O
at	O
a	O
given	O
time	O
.	O
</s>
<s>
If	O
the	O
element	O
this	O
node	O
was	O
a	O
winner	O
at	O
its	O
parent	B-Application
node	I-Application
,	O
then	O
the	O
element	O
and	O
certificates	O
at	O
the	O
parent	O
must	O
be	O
recursively	O
updated	O
too	O
.	O
</s>
<s>
It	O
may	O
also	O
trigger	O
changes	O
to	O
the	O
O(logn )	O
certificates	O
at	O
its	O
parent	B-Application
nodes	I-Application
.	O
</s>
<s>
Each	O
certificate	O
change	O
requires	O
a	O
delete	O
and	O
insert	O
operation	O
in	O
the	O
priority	B-Application
queue	I-Application
of	O
events	O
.	O
</s>
<s>
While	O
this	O
is	O
considered	O
responsive	O
in	O
general	O
,	O
it	O
is	O
less	O
responsive	O
than	O
other	O
kinetic	O
priority	B-Application
queues	I-Application
such	O
as	O
kinetic	B-Application
heaps	I-Application
which	O
respond	O
to	O
certificate	O
failures	O
with	O
O(1 )	O
certificate	O
changes	O
.	O
</s>
<s>
Locality	O
:	O
Each	O
element	O
is	O
involved	O
in	O
O(logn )	O
certificates	O
(	O
for	O
example	O
,	O
the	O
maximal	O
element	O
is	O
involved	O
in	O
a	O
certificate	O
at	O
each	O
of	O
its	O
parents	O
all	O
the	O
way	O
up	O
to	O
the	O
root	B-Application
node	I-Application
)	O
.	O
</s>
<s>
Again	O
,	O
while	O
this	O
is	O
considered	O
local	O
,	O
a	O
kinetic	B-Application
heap	I-Application
is	O
much	O
more	O
local	O
.	O
</s>
<s>
Efficiency	O
:	O
Kinetic	B-Application
heaps	I-Application
are	O
very	O
efficient	O
,	O
with	O
the	O
number	O
of	O
internal	O
events	O
(	O
certificate	O
changes	O
)	O
being	O
only	O
a	O
factor	O
of	O
O(log n )	O
more	O
than	O
the	O
number	O
of	O
external	O
events	O
.	O
</s>
<s>
Specifically	O
,	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-Data_Structure
tournament	I-Data_Structure
processes	O
events	O
in	O
time	O
,	O
where	O
is	O
a	O
Davenport-Schinzel	O
sequence	O
.	O
</s>
