<s>
A	O
Verlet	B-Algorithm
list	I-Algorithm
(	O
named	O
after	O
Loup	O
Verlet	O
)	O
is	O
a	O
data	O
structure	O
in	O
molecular	O
dynamics	O
simulations	O
to	O
efficiently	O
maintain	O
a	O
list	O
of	O
all	O
particles	O
within	O
a	O
given	O
cut-off	O
distance	O
of	O
each	O
other	O
.	O
</s>
<s>
This	O
method	O
may	O
easily	O
be	O
applied	O
to	O
Monte	B-Algorithm
Carlo	I-Algorithm
simulations	I-Algorithm
.	O
</s>
<s>
For	O
each	O
particle	O
,	O
a	O
Verlet	B-Algorithm
list	I-Algorithm
is	O
constructed	O
that	O
lists	O
all	O
other	O
particles	O
within	O
the	O
potential	O
cut-off	O
distance	O
,	O
plus	O
some	O
extra	O
distance	O
so	O
that	O
the	O
list	O
may	O
be	O
used	O
for	O
several	O
consecutive	O
Monte	O
Carlo	O
"	O
sweeps	O
"	O
(	O
set	O
of	O
Monte	O
Carlo	O
steps	O
or	O
moves	O
)	O
before	O
being	O
updated	O
.	O
</s>
<s>
If	O
we	O
wish	O
to	O
use	O
the	O
same	O
Verlet	B-Algorithm
list	I-Algorithm
times	O
before	O
updating	O
,	O
then	O
the	O
cut-off	O
distance	O
for	O
inclusion	O
in	O
the	O
Verlet	B-Algorithm
list	I-Algorithm
should	O
be	O
,	O
where	O
is	O
the	O
cut-off	O
distance	O
of	O
the	O
potential	O
,	O
and	O
is	O
the	O
maximum	O
Monte	O
Carlo	O
step	O
(	O
move	O
)	O
of	O
a	O
single	O
particle	O
.	O
</s>
<s>
Thus	O
,	O
we	O
will	O
spend	O
of	O
order	O
time	O
to	O
compute	O
the	O
Verlet	B-Algorithm
lists	I-Algorithm
(	O
is	O
the	O
total	O
number	O
of	O
particles	O
)	O
,	O
but	O
are	O
rewarded	O
with	O
Monte	O
Carlo	O
"	O
sweeps	O
"	O
of	O
order	O
instead	O
of	O
.	O
</s>
<s>
By	O
optimizing	O
our	O
choice	O
of	O
it	O
can	O
be	O
shown	O
that	O
Verlet	B-Algorithm
lists	I-Algorithm
allow	O
converting	O
the	O
problem	O
of	O
Monte	O
Carlo	O
sweeps	O
to	O
an	O
problem	O
.	O
</s>
<s>
Using	O
cell	B-Algorithm
lists	I-Algorithm
to	O
identify	O
the	O
nearest	O
neighbors	O
in	O
further	O
reduces	O
the	O
computational	O
cost	O
.	O
</s>
