<s>
The	O
-server	O
problem	O
is	O
a	O
problem	O
of	O
theoretical	O
computer	O
science	O
in	O
the	O
category	O
of	O
online	B-Algorithm
algorithms	I-Algorithm
,	O
one	O
of	O
two	O
abstract	O
problems	O
on	O
metric	O
spaces	O
that	O
are	O
central	O
to	O
the	O
theory	O
of	O
competitive	B-Algorithm
analysis	I-Algorithm
(	O
the	O
other	O
being	O
metrical	B-Algorithm
task	I-Algorithm
systems	I-Algorithm
)	O
.	O
</s>
<s>
In	O
this	O
problem	O
,	O
an	O
online	B-Algorithm
algorithm	I-Algorithm
must	O
control	O
the	O
movement	O
of	O
a	O
set	O
of	O
k	O
servers	O
,	O
represented	O
as	O
points	O
in	O
a	O
metric	O
space	O
,	O
and	O
handle	O
requests	O
that	O
are	O
also	O
in	O
the	O
form	O
of	O
points	O
in	O
the	O
space	O
.	O
</s>
<s>
The	O
most	O
prominent	O
open	O
question	O
concerning	O
the	O
k-server	B-Algorithm
problem	I-Algorithm
is	O
the	O
so-called	O
k-server	O
conjecture	O
,	O
also	O
posed	O
by	O
Manasse	O
et	O
al	O
.	O
</s>
<s>
This	O
conjecture	O
states	O
that	O
there	O
is	O
an	O
algorithm	O
for	O
solving	O
the	O
k-server	B-Algorithm
problem	I-Algorithm
in	O
an	O
arbitrary	O
metric	O
space	O
and	O
for	O
any	O
number	O
k	O
of	O
servers	O
that	O
has	O
competitive	B-Algorithm
ratio	I-Algorithm
exactly	O
k	O
.	O
Manasse	O
et	O
al	O
.	O
</s>
<s>
The	O
special	O
case	O
of	O
metrics	O
in	O
which	O
all	O
distances	O
are	O
equal	O
is	O
called	O
the	O
paging	O
problem	O
because	O
it	O
models	O
the	O
problem	O
of	O
page	B-General_Concept
replacement	I-General_Concept
algorithms	I-General_Concept
in	O
memory	O
caches	O
,	O
and	O
was	O
also	O
already	O
known	O
to	O
have	O
a	O
-competitive	O
algorithm	O
(	O
Sleator	O
and	O
Tarjan	O
1985	O
)	O
.	O
</s>
<s>
(	O
1990	O
)	O
first	O
proved	O
that	O
there	O
exists	O
an	O
algorithm	O
with	O
finite	O
competitive	B-Algorithm
ratio	I-Algorithm
for	O
any	O
constant	O
k	O
and	O
any	O
metric	O
space	O
,	O
and	O
finally	O
Koutsoupias	O
and	O
Papadimitriou	O
(	O
1995	O
)	O
proved	O
that	O
Work	O
Function	O
Algorithm	O
(	O
WFA	O
)	O
has	O
competitive	B-Algorithm
ratio	I-Algorithm
2k	O
-	O
1	O
.	O
</s>
<s>
However	O
,	O
despite	O
the	O
efforts	O
of	O
many	O
other	O
researchers	O
,	O
reducing	O
the	O
competitive	B-Algorithm
ratio	I-Algorithm
to	O
or	O
providing	O
an	O
improved	O
lower	O
bound	O
remains	O
open	O
.	O
</s>
<s>
As	O
a	O
k-server	B-Algorithm
problem	I-Algorithm
,	O
the	O
servers	O
are	O
the	O
technicians	O
,	O
so	O
k	O
=	O
2	O
and	O
this	O
is	O
a	O
2-server	O
problem	O
.	O
</s>
<s>
The	O
competitive	B-Algorithm
ratio	I-Algorithm
of	O
our	O
algorithm	O
on	O
this	O
input	O
is	O
20,500	O
/6000	O
or	O
approximately	O
3.4	O
,	O
and	O
by	O
adjusting	O
the	O
parameters	O
of	O
this	O
example	O
the	O
competitive	B-Algorithm
ratio	I-Algorithm
of	O
this	O
algorithm	O
can	O
be	O
made	O
arbitrarily	O
large	O
.	O
</s>
