quad_mesh_rcm, a C++ code which computes the reverse Cuthill-McKee (RCM) reordering for nodes in a mesh of 4-node quadrilaterals.

The user supplies a node file and an element file, containing the coordinates of the nodes, and the indices of the nodes that make up each element.

The program reads the data, computes the adjacency information, carries out the RCM algorithm to get the permutation, applies the permutation to the nodes and elements, and writes out new node and element files that correspond to the RCM permutation.

Note that, internally, the program has to convert some data from 0-based to 1-based indexing in order to work with the RCM codes. Aside from some inelegant coding, the user should not notice any effects of this temporary adjustment.


quad_mesh_rcm 'prefix'
where 'prefix' is the common file prefix:


The computer code and data files described and made available on this web page are distributed under the MIT license


quad_mesh_rcm is available in a C++ version and a FORTRAN version and a MATLAB version.

Related Data and Programs:

MESH_BANDWIDTH, a C++ code which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension.

MESH_DISPLAY_OPENGL, a C++ code which reads files defining a polygonal mesh and displays an image using OpenGL.

QUAD_MESH, a data directory which defines a format for storing meshes of quadrilaterals over a 2D region.

QUAD_MESH, a C++ code which handles meshes of quadrilaterals over a 2D region;


RCM, a C++ code which carries out reverse Cuthill-McKee computations.

TET_MESH_RCM, a C++ code which applies the reverse Cuthill-McKee reordering to a tetrahedral mesh of nodes in 3D.

TRIANGULATION_RCM, a C++ code which reads files describing a triangulation of nodes in 2D, and applies the RCM algorithm to produce a renumbering of the triangulation with a reduced bandwidth.


  1. HL Crane, Norman Gibbs, William Poole, Paul Stockmeyer,
    Algorithm 508: Matrix Bandwidth and Profile Reduction,
    ACM Transactions on Mathematical Software,
    Volume 2, Number 4, December 1976, pages 375-377.
  2. Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
    Computational Geometry,
    Springer, 2000,
    ISBN: 3-540-65620-0.
  3. Alan George, Joseph Liu,
    Computer Solution of Large Sparse Positive Definite Matrices,
    Prentice Hall, 1981,
    ISBN: 0131652745,
    LC: QA188.G46
  4. Norman Gibbs,
    Algorithm 509: A Hybrid Profile Reduction Algorithm,
    ACM Transactions on Mathematical Software,
    Volume 2, Number 4, December 1976, pages 378-387.
  5. Norman Gibbs, William Poole, Paul Stockmeyer,
    An Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix,
    SIAM Journal on Numerical Analysis,
    Volume 13, 1976, pages 236-250.
  6. Joseph ORourke,
    Computational Geometry,
    Second Edition,
    Cambridge, 1998,
    ISBN: 0521649765,
    LC: QA448.D38.

Source Code:

Last revised on 04 April 2020.