<s>
In	O
numerical	O
linear	O
algebra	O
,	O
the	O
Cuthill	B-Algorithm
–	I-Algorithm
McKee	I-Algorithm
algorithm	I-Algorithm
(	O
CM	O
)	O
,	O
named	O
after	O
Elizabeth	O
Cuthill	O
and	O
James	O
McKee	O
,	O
is	O
an	O
algorithm	O
to	O
permute	O
a	O
sparse	B-Algorithm
matrix	I-Algorithm
that	O
has	O
a	O
symmetric	B-Algorithm
sparsity	B-Algorithm
pattern	O
into	O
a	O
band	B-Algorithm
matrix	I-Algorithm
form	O
with	O
a	O
small	O
bandwidth	B-Algorithm
.	O
</s>
<s>
The	O
reverse	B-Algorithm
Cuthill	I-Algorithm
–	I-Algorithm
McKee	I-Algorithm
algorithm	I-Algorithm
(	O
RCM	O
)	O
due	O
to	O
Alan	O
George	O
and	O
Joseph	O
Liu	O
is	O
the	O
same	O
algorithm	O
but	O
with	O
the	O
resulting	O
index	O
numbers	O
reversed	O
.	O
</s>
<s>
Given	O
a	O
symmetric	B-Algorithm
matrix	O
we	O
visualize	O
the	O
matrix	O
as	O
the	O
adjacency	B-Algorithm
matrix	I-Algorithm
of	O
a	O
graph	O
.	O
</s>
<s>
The	O
Cuthill	B-Algorithm
–	I-Algorithm
McKee	I-Algorithm
algorithm	I-Algorithm
is	O
then	O
a	O
relabeling	O
of	O
the	O
vertices	O
of	O
the	O
graph	O
to	O
reduce	O
the	O
bandwidth	B-Algorithm
of	O
the	O
adjacency	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
In	O
other	O
words	O
,	O
number	O
the	O
vertices	O
according	O
to	O
a	O
particular	O
level	O
structure	O
(	O
computed	O
by	O
breadth-first	B-Algorithm
search	I-Algorithm
)	O
where	O
the	O
vertices	O
in	O
each	O
level	O
are	O
visited	O
in	O
order	O
of	O
their	O
predecessor	O
's	O
numbering	O
from	O
lowest	O
to	O
highest	O
.	O
</s>
