<s>
The	O
List	O
Update	O
or	O
the	O
List	O
Access	O
problem	O
is	O
a	O
simple	O
model	O
used	O
in	O
the	O
study	O
of	O
competitive	B-Algorithm
analysis	I-Algorithm
of	O
online	B-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
a	O
Linked	B-Data_Structure
List	I-Data_Structure
,	O
and	O
a	O
request	O
sequence	O
of	O
accesses	O
,	O
the	O
problem	O
is	O
to	O
come	O
up	O
with	O
a	O
strategy	O
of	O
reordering	O
the	O
list	O
so	O
that	O
the	O
total	O
cost	O
of	O
accesses	O
is	O
minimized	O
.	O
</s>
<s>
An	O
online	B-Algorithm
algorithm	I-Algorithm
for	O
this	O
problem	O
has	O
to	O
reorder	O
the	O
elements	O
and	O
serve	O
requests	O
based	O
only	O
on	O
the	O
knowledge	O
of	O
previously	O
requested	O
items	O
and	O
hence	O
its	O
strategy	O
may	O
not	O
have	O
the	O
optimum	O
cost	O
as	O
compared	O
to	O
an	O
offline	B-Algorithm
algorithm	I-Algorithm
that	O
gets	O
to	O
see	O
the	O
entire	O
request	O
sequence	O
and	O
devise	O
a	O
complete	O
strategy	O
before	O
serving	O
the	O
first	O
request	O
.	O
</s>
<s>
Along	O
with	O
its	O
original	O
uses	O
,	O
this	O
problem	O
has	O
been	O
suggested	O
to	O
have	O
a	O
strong	O
similarity	O
to	O
problems	O
of	O
improving	O
global	O
context	O
and	O
compressibility	O
following	O
a	O
Burrows	B-Algorithm
–	I-Algorithm
Wheeler	I-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
An	O
adversary	B-Algorithm
is	O
an	O
entity	O
that	O
gets	O
to	O
choose	O
the	O
request	O
sequence	O
for	O
an	O
algorithm	O
ALG	O
.	O
</s>
<s>
Depending	O
on	O
whether	O
can	O
be	O
changed	O
based	O
on	O
the	O
strategy	O
of	O
ALG	O
,	O
adversaries	B-Algorithm
are	O
given	O
various	O
powers	O
,	O
and	O
the	O
performance	O
of	O
ALG	O
is	O
measured	O
against	O
these	O
adversaries	B-Algorithm
.	O
</s>
<s>
An	O
adaptive	O
online	O
adversary	B-Algorithm
gets	O
to	O
make	O
the	O
next	O
request	O
based	O
on	O
the	O
previous	O
results	O
of	O
the	O
online	B-Algorithm
algorithm	I-Algorithm
,	O
but	O
pays	O
for	O
the	O
request	O
optimally	O
and	O
online	O
.	O
</s>
<s>
An	O
adaptive	O
offline	O
adversary	B-Algorithm
gets	O
to	O
make	O
the	O
next	O
request	O
based	O
on	O
the	O
previous	O
results	O
of	O
the	O
online	B-Algorithm
algorithm	I-Algorithm
,	O
but	O
pays	O
the	O
optimal	O
offline	O
cost	O
.	O
</s>
<s>
Competitive	B-Algorithm
analysis	I-Algorithm
for	O
many	O
list	B-Algorithm
update	I-Algorithm
problems	I-Algorithm
were	O
carried	O
out	O
without	O
any	O
specific	O
knowledge	O
of	O
the	O
exact	O
nature	O
of	O
the	O
optimum	O
offline	B-Algorithm
algorithm	I-Algorithm
(	O
OPT	O
)	O
.	O
</s>
<s>
The	O
best	O
known	O
optimal	O
offline	B-Algorithm
algorithm	I-Algorithm
dependent	O
on	O
request	O
sequence	O
length	O
runs	O
in	O
O( l^2( l−1	O
)	O
!	O
n	O
)	O
time	O
published	O
by	O
Dr	O
Srikrishnan	O
Divakaran	O
in	O
2014	O
.	O
</s>
<s>
An	O
optimal	O
offline	B-Algorithm
algorithm	I-Algorithm
using	O
only	O
free	O
exchanges	O
would	O
cost	O
9	O
(	O
3+3+2+1	O
)	O
,	O
whereas	O
an	O
optimal	O
offline	B-Algorithm
algorithm	I-Algorithm
using	O
only	O
paid	O
exchanges	O
would	O
cost	O
8	O
.	O
</s>
<s>
So	O
,	O
we	O
cannot	O
get	O
away	O
with	O
just	O
using	O
free	O
transpositions	O
for	O
the	O
optimum	O
offline	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
The	O
optimum	O
list	B-Algorithm
update	I-Algorithm
problem	I-Algorithm
was	O
proven	O
to	O
be	O
NP-hard	O
by	O
.	O
</s>
<s>
An	O
online	B-Algorithm
algorithm	I-Algorithm
ALG	O
has	O
a	O
competitive	B-Algorithm
ratio	I-Algorithm
c	O
if	O
for	O
any	O
input	O
it	O
performs	O
at	O
least	O
as	O
good	O
as	O
c	O
times	O
worse	O
than	O
OPT	O
.	O
</s>
<s>
Online	B-Algorithm
algorithms	I-Algorithm
can	O
either	O
be	O
deterministic	O
or	O
randomized	O
and	O
it	O
turns	O
out	O
that	O
randomization	O
in	O
this	O
case	O
can	O
truly	O
help	O
against	O
oblivious	O
adversaries	B-Algorithm
.	O
</s>
<s>
In	O
a	O
classic	O
result	O
using	O
Potential	B-General_Concept
method	I-General_Concept
analysis	O
proved	O
that	O
MTF	O
is	O
2-competitive	O
.	O
</s>
<s>
The	O
type	O
of	O
adversary	B-Algorithm
does	O
n't	O
matter	O
in	O
the	O
case	O
of	O
deterministic	O
algorithms	O
,	O
because	O
the	O
adversary	B-Algorithm
can	O
run	O
a	O
copy	O
of	O
the	O
deterministic	O
algorithm	O
on	O
their	O
own	O
to	O
precompute	O
the	O
most	O
disastrous	O
sequence	O
.	O
</s>
<s>
It	O
turns	O
out	O
that	O
BIT	O
breaks	O
the	O
deterministic	O
bound	O
-	O
it	O
is	O
better	O
than	O
MTF	O
against	O
oblivious	O
adversaries	B-Algorithm
.	O
</s>
<s>
The	O
list	B-Algorithm
update	I-Algorithm
problem	I-Algorithm
where	O
elements	O
maybe	O
inserted	O
and	O
deleted	O
is	O
called	O
the	O
dynamic	B-Data_Structure
list	B-Algorithm
update	I-Algorithm
problem	I-Algorithm
,	O
as	O
opposed	O
to	O
the	O
static	O
list	B-Algorithm
update	I-Algorithm
problem	I-Algorithm
where	O
only	O
accessing	O
list	O
elements	O
are	O
allowed	O
.	O
</s>
