Cuthill–McKee algorithm: Difference between revisions

Revision as of 20:04, 12 December 2011

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<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 matrix into a banded form with a small

[[bandwidth (matrix theory)|bandwidth]] of [[sparse matrix|sparse]] [[symmetric matrix|symmetric matrices]]. The '''reverse Cuthill–McKee algorithm''' ('''RCM''') due to Alan George is the same algorithm but with the resulting index numbers reversed. In practice this generally results in less [[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>

[[File:can_73_orig.pdf|thumb|Original matrix from Harwell-Boeing collection]]

[[File:can_73_cm.pdf|thumb|Cuthill-McKee ordering of the same matrix]]

[[File:can_73_rcm.pdf|thumb|RCM ordering of the same matrix]]

==Algorithm==