An Experimental Analysis of Three Pseudo-peripheral Vertex Finders in conjunction with the Reverse Cuthill-McKee Method for Bandwidth Reduction

Sanderson L. Gonzaga de Oliveira, Alexandre A. A. M. Abreu

Abstract


The need to determine pseudoperipheral vertices arises from several graph-theoretical approaches for ordering sparse matrix equations. Results of two algorithms for finding such vertices, namely, the George-Liu and Kaveh-Bondarabady algorithms, are evaluated in this work along with a variant of the Kaveh-Bondarabady algorithm. Experiments among these three algorithms in conjunction with the Reverse Cuthill-McKee method suggest that the modified algorithm is a suitable alternative for reducing bandwidth of matrices that arise from specific application area, but it is dominated by the well-know George-Liu algorithm mainly when considering the computational times of the algorithms.

Keywords


sparse matrices; Graph labeling; Graph algorithm; Reverse Cuthill-McKee method; Bandwidth reduction; Graph theory

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References


I. Arany, L. Szoda, and W. Smyth. An improved method for reducing the

bandwidth of sparse symmetric matrices. In IFIP Congress, pp. 1246–1250,

Ljubljana, Yugoslavia, 1971.

I. Arany. An efficient algorithm for finding peripheral nodes. In L. Lovász and E. Szemerédi, editors, Colloquia Mathematica Societatis János Bolyai (Hungarian Edition), Theory of Algorithms Pécs, volume 44, pages 27–35. North-Holland, Budapest, 1984.

M. Benzi and D. B. Szyld and A. van Duin. Orderings for incomplete factorization preconditioning of nonsymmetric problems, SIAM Journal on Scientific Computing, 20(5):1652–1670, 1999.

J. A. B. Bernardes and S. L. Gonzaga de Oliveira. A systematic review of

heuristics for profile reduction of symmetric matrices. Procedia Comput. Sci.,

:221–230, 2015.

Boost. Boost C++ Libraries. http://www.boost.org/, 2017, accessed: 2017-

-28.

J. J. Camata, A. L. Rossa, A. M. P. Valli, L. Catabriga, G. F. Carey, and A.

L. G. A. Coutinho. Reordering and incomplete preconditioning in serial and

parallel adaptive mesh refinement and coarsening flow solutions. International Journal for Numerical Methods in Fluids, 69:802–823, 2012.

G. O. Chagas and S. L. Gonzaga de Oliveira. Metaheuristic-based heuristics for symmetric-matrix bandwidth reduction: a systematic review. Procedia Computer Science, 51:211–220, 2015.

T. A. Davis and Y. Hu. The University of Florida sparse matrix collection.

ACM Transactions on Mathematical Software, 38(1):1–25, 2011.

I. S. Duff and G. A. Meurant. The effect of ordering on preconditioned conju-

gate gradients. BIT Numerical Mathematics, 16(3):263–270, 1989.

I. S. Duff, J. K. Reid, and J. A. Scott. The use of profile reduction algorithms

with a frontal code. International Journal of Numerical Methods in Engineering, 28(11):2555–2568, 1989.

A. George, Computer Implementation of the Finite Element Method. PhD

thesis, Stanford University, 1971.

A. George and J. W. H. Liu. An implementation of a pseudoperipheral node

finder. ACM Transactions on Mathematical Software, 5(3):284–295, 1979.

A. George and J. W. Liu Computer solution of large sparse positive definite

systems. Prentice-Hall, Englewood Cliffs, 1981.

N. E. Gibbs, W. G. Poole, and P. K. Stockmeyer. An algorithm for reducing

the bandwidth and profile of a sparse matrix. SIAM Journal on Numerical

Analysis, 13(2):236–250, 1976.

J. R. Gilbert and C. Moler and R. Schreiber. Sparse Matrices in MATLAB:

Design and Implementation. SIAM Journal on Matrix Analysis, 3(1):333–356,

A. Kaveh and H. A. Rahimi Bondarabady. Ordering for wavefront optimization. Computer & Structure, 78:227–235, 2000.

The MathWorks, Inc. MATLAB. http://www.mathworks.com/products/

matlab, 1994–2017.

J. W. Eaton and D. Bateman and S. Hauberg and R. Wehbring. GNU Octave

version 4.0.0 manual: a high-level interactive language for numerical computations, http://www.gnu.org/software/octave/doc/interpreter, 2015.

J. K. Reid and J. A. Scott. Ordering symmetric sparse matrices for small profile and wavefront. International Journal for Numerical Methods in Engineering, 45(12):1737–1755, 1999.




DOI: https://doi.org/10.5540/tema.2019.020.03.497

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