<s>
A	O
Kinetic	B-Application
hanger	I-Application
is	O
a	O
randomized	O
version	O
of	O
a	O
kinetic	B-Application
heap	I-Application
whose	O
performance	O
is	O
easy	O
to	O
analyze	O
tightly	O
.	O
</s>
<s>
A	O
kinetic	B-Application
hanger	I-Application
satisfies	O
the	O
heap	B-Application
property	I-Application
(	O
the	O
priority	O
of	O
each	O
element	O
is	O
higher	O
than	O
the	O
priority	O
of	O
its	O
children	O
)	O
but	O
relaxes	O
the	O
requirement	O
that	O
the	O
tree	B-Application
structure	O
must	O
be	O
strictly	O
balanced	O
,	O
thus	O
insertions	O
and	O
deletions	O
can	O
be	O
randomized	O
.	O
</s>
<s>
As	O
a	O
result	O
,	O
the	O
structure	O
of	O
the	O
kinetic	B-Application
hanger	I-Application
has	O
the	O
property	O
that	O
it	O
is	O
drawn	O
uniformly	O
at	O
random	O
from	O
the	O
space	O
of	O
all	O
possible	O
heap-like	O
structures	O
on	O
its	O
elements	O
.	O
</s>
<s>
The	O
kinetic	B-Application
hanger	I-Application
structure	O
(	O
including	O
certificates	O
and	O
event	O
queue	O
)	O
is	O
exactly	O
the	O
same	O
as	O
the	O
kinetic	B-Application
heap	I-Application
structure	O
,	O
but	O
without	O
the	O
balancing	O
requirement	O
.	O
</s>
<s>
Thus	O
,	O
it	O
consists	O
of	O
an	O
efficient	O
priority	O
queue	O
(	O
the	O
event	O
queue	O
)	O
to	O
maintain	O
the	O
certificate	O
failure	O
times	O
,	O
as	O
well	O
as	O
a	O
main	O
(	O
not	O
necessarily	O
balanced	O
)	O
heap-like	O
tree	B-Application
structure	O
in	O
which	O
the	O
elements	O
are	O
stored	O
.	O
</s>
<s>
There	O
is	O
a	O
certificate	O
associated	O
with	O
each	O
edge	O
that	O
enforces	O
the	O
heap	B-Application
property	I-Application
(	O
priority	O
of	O
parent	O
>	O
priority	O
of	O
child	O
)	O
along	O
that	O
edge	O
.	O
</s>
<s>
The	O
characteristic	O
operation	O
in	O
a	O
kinetic	B-Application
hanger	I-Application
is	O
"	O
hanging	O
"	O
,	O
which	O
is	O
defined	O
as	O
follows	O
(	O
a	O
distinction	O
is	O
made	O
between	O
a	O
node	O
in	O
the	O
tree	B-Application
structure	O
and	O
the	O
element	O
stored	O
in	O
it	O
)	O
.	O
</s>
<s>
The	O
main	O
difference	O
between	O
the	O
kinetic	B-Application
hanger	I-Application
and	O
the	O
kinetic	B-Application
heap	I-Application
is	O
in	O
the	O
key	O
operations	O
,	O
which	O
are	O
implemented	O
as	O
follows	O
in	O
a	O
kinetic	B-Application
hanger	I-Application
:	O
</s>
<s>
This	O
takes	O
O(n log n )	O
time	O
,	O
similar	O
to	O
a	O
kinetic	B-Application
heap	I-Application
.	O
</s>
<s>
Insert	O
:	O
The	O
kinetic	B-Application
hanger	I-Application
inserts	O
top-down	O
(	O
instead	O
of	O
bottom-up	O
)	O
by	O
"	O
hanging	O
"	O
the	O
new	O
element	O
at	O
the	O
root	B-Application
node	I-Application
.	O
</s>
<s>
Delete	O
:	O
This	O
is	O
a	O
simpler	O
operation	O
than	O
in	O
a	O
heap	B-Application
,	O
since	O
the	O
balancing	O
of	O
tree	B-Application
structure	O
does	O
n't	O
need	O
to	O
be	O
maintained	O
.	O
</s>
