<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
the	O
ski	B-Algorithm
rental	I-Algorithm
problem	I-Algorithm
is	O
a	O
name	O
given	O
to	O
a	O
class	O
of	O
problems	O
in	O
which	O
there	O
is	O
a	O
choice	O
between	O
continuing	O
to	O
pay	O
a	O
repeating	O
cost	O
or	O
paying	O
a	O
one-time	O
cost	O
which	O
eliminates	O
or	O
reduces	O
the	O
repeating	O
cost	O
.	O
</s>
<s>
Ski	B-Algorithm
rental	I-Algorithm
is	O
one	O
example	O
where	O
the	O
rent/buy	O
is	O
the	O
entire	O
problem	O
.	O
</s>
<s>
This	O
is	O
an	O
instance	O
of	O
a	O
randomized	B-General_Concept
algorithm	I-General_Concept
.	O
</s>
<s>
A	O
randomized	B-General_Concept
algorithm	I-General_Concept
can	O
be	O
understood	O
as	O
a	O
composition	O
of	O
different	O
algorithms	O
,	O
each	O
one	O
which	O
occurs	O
with	O
a	O
given	O
probability	O
.	O
</s>
<s>
We	O
define	O
the	O
expected	O
competitive	B-Algorithm
ratio	I-Algorithm
on	O
a	O
given	O
instance	O
i	O
as	O
:	O
</s>
<s>
,	O
where	O
is	O
the	O
competitive	B-Algorithm
ratio	I-Algorithm
for	O
instance	O
i	O
,	O
given	O
.	O
</s>
<s>
Consequently	O
,	O
the	O
competitive	B-Algorithm
ratio	I-Algorithm
of	O
a	O
randomized	B-General_Concept
algorithm	I-General_Concept
is	O
given	O
by	O
the	O
worst	O
value	O
of	O
over	O
all	O
given	O
instances	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
the	O
coin	O
flipping	O
ski-rental	O
,	O
we	O
note	O
that	O
the	O
randomized	B-General_Concept
algorithm	I-General_Concept
has	O
2	O
possible	O
branches	O
:	O
If	O
the	O
coin	O
comes	O
up	O
heads	O
,	O
we	O
buy	O
on	O
day	O
8	O
,	O
otherwise	O
we	O
buy	O
on	O
day	O
10	O
.	O
</s>
<s>
Therefore	O
,	O
the	O
competitive	B-Algorithm
ratio	I-Algorithm
of	O
the	O
randomized	O
ski-rental	O
coin	O
flipping	O
algorithm	O
is	O
1.8	O
.	O
</s>
<s>
The	O
best	O
randomized	B-General_Concept
algorithm	I-General_Concept
against	O
an	O
oblivious	B-Algorithm
adversary	I-Algorithm
is	O
to	O
choose	O
some	O
day	O
i	O
at	O
random	O
according	O
to	O
the	O
following	O
distribution	O
p	O
,	O
rent	O
for	O
i-1	O
days	O
and	O
buy	O
skis	O
on	O
the	O
morning	O
of	O
day	O
i	O
if	O
one	O
are	O
still	O
up	O
for	O
skiing	O
.	O
</s>
<s>
No	O
randomized	B-General_Concept
algorithm	I-General_Concept
can	O
do	O
better	O
.	O
</s>
<s>
Snoopy	B-General_Concept
caching	I-General_Concept
:	O
several	O
caches	O
share	O
the	O
same	O
memory	O
space	O
that	O
is	O
partitioned	O
into	O
blocks	O
.	O
</s>
<s>
The	O
two	O
cache	O
,	O
one	O
block	O
snoopy	B-General_Concept
caching	I-General_Concept
problem	O
is	O
just	O
the	O
ski	B-Algorithm
rental	I-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
described	O
a	O
one-parameter	O
family	O
of	O
inputs	O
,	O
called	O
the	O
basis	O
inputs	O
,	O
and	O
showed	O
that	O
when	O
restricted	O
to	O
these	O
basis	O
inputs	O
,	O
the	O
TCP	O
acknowledgement	O
problem	O
behaves	O
the	O
same	O
as	O
the	O
ski	B-Algorithm
rental	I-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
This	O
simplified	O
problem	O
may	O
be	O
viewed	O
as	O
a	O
continuous	O
version	O
of	O
the	O
ski	B-Algorithm
rental	I-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
is	O
a	O
ski	B-Algorithm
rental	I-Algorithm
problem	I-Algorithm
.	O
</s>
