Cuthill–McKee algorithm: Difference between revisions

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Revision as of 00:41, 16 January 2022

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[[File:Can 73 rcm.svg|thumb|RCM ordering of the same matrix]]

In [[numerical linear algebra]], the '''Cuthill–McKee algorithm''' ('''CM'''), named for [[Elizabeth Cuthill]] and James<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 and Joseph Liu is the same algorithm but with the resulting index numbers reversed.<ref>{{cite web |url=http://ciprian-zavoianu.blogspot.ch/2009/01/project-bandwidth-reduction.html |title = Ciprian Zavoianu - weblog: Tutorial: Bandwidth reduction - The CutHill-McKee Algorithm}}</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]]