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A Variant of the George-Liu Algorithm

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Book cover Computational Science and Its Applications – ICCSA 2019 (ICCSA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11619))

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Abstract

This paper evaluates a variant of the George-Liu algorithm for finding a pseudoperipheral vertex in a graph aiming at returning a vertex having a larger eccentricity than the original algorithm. The experiments show that the Reverse Cuthill-McKee method with ordering started with vertices given by the new variant of the George-Liu algorithm yields promising results when applied to small symmetric matrices.

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Notes

  1. 1.

    https://www.mathworks.com/help/matlab/ref/symrcm.html?requestedDomain=www.mathworks.com, https://octave.sourceforge.io/octave/function/symrcm.html.

  2. 2.

    http://www.boost.org/doc/libs/1_38_0/libs/graph/doc/cuthill_mckee_ordering.html.

References

  1. Benzi, M., Szyld, D.B., Van Duin, A.: Orderings for incomplete factorization preconditioning of nonsymmetric problems. SIAM J. Sci. Comput. 20(5), 1652–1670 (1999)

    Article  MathSciNet  Google Scholar 

  2. Camata, J.J., Rossa, A.L., Valli, A.M.P., Catabriga, L., Carey, G.F., Coutinho, A.L.G.A.: Reordering and incomplete preconditioning in serial and parallel adaptive mesh refinement and coarsening flow solutions. Int. J. Numer. Meth. Fluids 69(4), 802–823 (2012)

    Article  MathSciNet  Google Scholar 

  3. Chagas, G.O., Gonzaga de Oliveira, S.L.: Metaheuristic-based heuristics for symmetric-matrix bandwidth reduction: a systematic review. Procedia Comput. Sci. 51, 211–220 (2015). https://doi.org/10.1016/j.procs.2015.05.229

    Article  Google Scholar 

  4. Gonzaga de Oliveira, S.L., Bernardes, J.A.B., Chagas, G.O.: An evaluation of reordering algorithms to reduce the computational cost of the incomplete Cholesky-conjugate gradient method. Comput. Appl. Math. 37(3), 2965–3004 (2018)

    Article  MathSciNet  Google Scholar 

  5. Gonzaga de Oliveira, S.L., Bernardes, J.A.B., Chagas, G.O.: An evaluation of low-cost heuristics for matrix bandwidth and profile reductions. Comput. Appl. Math. 37, 1412–1471 (2018)

    Article  MathSciNet  Google Scholar 

  6. Bernardes, J.A.B., Gonzaga de Oliveira, S.L.: A systematic review of heuristics for profile reduction of symmetric matrices. Procedia Comput. Sci. 51, 221–230 (2015)

    Article  Google Scholar 

  7. Kaveh, A., Bijari, S.: Bandwidth, profile and wavefront optimization using PSO, CBO, ECBO and TWO algorithms. Iran. J. Sci. Technol. Trans. Civ. Eng. 41(1), 1–12 (2017)

    Article  Google Scholar 

  8. Kaveh, A.: Bandwidth, profile, and wavefront optimization using CBO, ECBO, and TWO algorithms. Applications of Metaheuristic Optimization Algorithms in Civil Engineering, pp. 235–256. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-48012-1_13

    Chapter  MATH  Google Scholar 

  9. George, A.: Computer implementation of the finite element method. Ph.D. thesis, Stanford University, Stanford (1971)

    Google Scholar 

  10. George, A., Liu, J.W.H.: An implementation of a pseudoperipheral node finder. ACM Trans. Math. Softw. 5(3), 284–295 (1979)

    Article  Google Scholar 

  11. George, A., Liu, J.W.: Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall, Englewood Cliffs (1981)

    MATH  Google Scholar 

  12. Gonzaga de Oliveira, S.L., Abreu, A.A.A.M., Robaina, D.T., Kischnhevsky, M.: An evaluation of four reordering algorithms to reduce the computational cost of the Jacobi-preconditioned conjugate gradient method using high-precision arithmetic. Int. J. Bus. Intell. Data Min. 12(2), 190–209 (2017)

    Article  Google Scholar 

  13. Gilbert, J.R., Moler, C., Schreiber, R.: Sparse matrices in MATLAB: design and implementation. SIAM J. Matrix Anal. 3(1), 333–356 (1992)

    Article  MathSciNet  Google Scholar 

  14. The MathWorks, Inc.: MATLAB (1994–2018). http://www.mathworks.com/products/matlab/

  15. Eaton, J.W., Bateman, D., Hauberg, S., Wehbring, R.: GNU Octave version 4.0.0 manual: a high-level interactive language for numerical computations (2015)

    Google Scholar 

  16. Boost: Boost C++ libraries (2017). http://www.boost.org/. Accessed 28 June 2017

  17. Reid, J.K., Scott, J.A.: Ordering symmetric sparse matrices for small profile and wavefront. Int. J. Numer. Meth. Eng. 45(12), 1737–1755 (1999)

    Article  Google Scholar 

  18. Cuthill, E., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. In: ACM Proceedings of the 1969 24th International Conference, pp. 157–172. ACM, New York (1969)

    Google Scholar 

  19. Davis, T.A., Hu, Y.: The University of Florida sparse matrix collection. ACM Trans. Math. Softw. 38(1), 1–25 (2011)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Universidade Federal de Lavras, Lavras, MG, Brazil

    S. L. Gonzaga de Oliveira

  2. Instituto Federal de Educação, Ciência e Tecnologia de Santa Catarina, Canoinhas, SC, Brazil

    A. A. A. M. Abreu

  3. Laboratório Nacional de Computação Científica (LNCC), Petropólis, RJ, Brazil

    C. Osthoff

  4. Universidade do Estado do Rio de Janeiro, Nova Friburgo, RJ, Brazil

    L. N. Henderson Guedes de Oliveira

Authors
  1. S. L. Gonzaga de Oliveira
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  2. A. A. A. M. Abreu
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  3. C. Osthoff
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  4. L. N. Henderson Guedes de Oliveira
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Corresponding author

Correspondence to S. L. Gonzaga de Oliveira .

Editor information

Editors and Affiliations

  1. Covenant University, Ota, Nigeria

    Sanjay Misra

  2. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  3. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  4. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  5. Saint Petersburg State University, Saint Petersburg, Russia

    Vladimir Korkhov

  6. Polytechnic University of Bari, Bari, Italy

    Carmelo Torre

  7. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  8. Monash University, Clayton, VIC, Australia

    David Taniar

  9. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  10. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

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Gonzaga de Oliveira, S.L., Abreu, A.A.A.M., Osthoff, C., Henderson Guedes de Oliveira, L.N. (2019). A Variant of the George-Liu Algorithm. In: Misra, S., et al. Computational Science and Its Applications – ICCSA 2019. ICCSA 2019. Lecture Notes in Computer Science(), vol 11619. Springer, Cham. https://doi.org/10.1007/978-3-030-24289-3_1

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  • DOI: https://doi.org/10.1007/978-3-030-24289-3_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24288-6

  • Online ISBN: 978-3-030-24289-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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