Cuthill–McKee algorithm: Difference between revisions

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Revision as of 08:19, 20 April 2013

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[[File:can_73_cmcan 73 cm.pdf|thumb|Cuthill-McKee ordering of the same matrix]]

[[File:can_73_rcmcan 73 rcm.pdf|thumb|RCM ordering of the same matrix]]

In the [[mathematics|mathematical]] subfield of [[Matrix (mathematics)|matrix theory]], the '''Cuthill–McKee algorithm''' (named for Elizabeth Cuthill and J. 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. 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]]

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by listing all vertices adjacent to all nodes in <math> R_i </math>. These

nodes are listed in increasing degree. This last detail is the only difference

with the breadth-first search algorithm.

==Algorithm==

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==References==

<references />

* [http://www.boost.org/doc/libs/1_37_0/libs/graph/doc/cuthill_mckee_ordering.html Cuthill–McKee documentation] for the [[Boost C++ Libraries]].

* [http://ciprian-zavoianu.blogspot.com/2009/01/project-bandwidth-reduction.html A detailed description of the Cuthill–McKee algorithm].

{{DEFAULTSORT:Cuthill-McKee algorithm}}

[[Category:Matrix theory]]

[[Category:Graph algorithms]]