[[File:can 73 rcm svg.svg|thumb|RCM ordering of the same matrix]]
In [[numerical linear algebra]], the '''Cuthill–McKee algorithm''' ('''CM'''), named for Elizabeth Cuthill and JJames<ref name="mckee">[http://calhoun.nps.edu/bitstream/handle/10945/30131/recommendationsf00fran.pdf''Recommendations for ship hull surface representation''], page 6</ref> McKee,<ref name="cm">E. Cuthill and J. McKee. [http://portal.acm.org/citation.cfm?id=805928''Reducing the bandwidth of sparse symmetric matrices''] In Proc. 24th Nat. Conf. [[Association for Computing Machinery|ACM]], pages 157–172, 1969.</ref> is an [[algorithm]] to permute a [[sparse matrix]] that has a [[symmetric matrix|symmetric]] sparsity pattern into a [[band matrix]] form with a small [[bandwidth (matrix theory)|bandwidth]]. The '''reverse Cuthill–McKee algorithm''' ('''RCM''') due to Alan George is the same algorithm but with the resulting index numbers reversed.<ref>http://ciprian-zavoianu.blogspot.ch/2009/01/project-bandwidth-reduction.html</ref> In practice this generally results in less [[Sparse matrix#Reducing fill-in|fill-in]] than the CM ordering when Gaussian elimination is applied.<ref name="gl">J. A. George and J. W-H. Liu, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, 1981</ref>
The Cuthill McKee algorithm is a variant of the standard [[breadth-first search]]
