Advertisement

A Memetic Algorithm for Vertex-Biconnectivity Augmentation

  • Sandor Kersting
  • Günther R. Raidl
  • Ivana Ljubić
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2279)

Abstract

This paper considers the problem of augmenting a given graph by a cheapest possible set of additional edges in order to make the graph vertex-biconnected. A real-world instance of this problem is the enhancement of an already established computer network to become robust against single node failures. The presented memetic algorithm includes an effective preprocessing of problem data and a fast local improvement strategy which is applied during initialization, mutation, and recombination. Only feasible, locally optimal solutions are created as candidates. Empirical results indicate the superiority of the new approach over two previous heuristics and an earlier evolutionary method.

Keywords

Minimum Span Tree Memetic Algorithm Hybrid Genetic Algorithm Local Improvement Augmentation Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K. P. Eswaran and R. E. Tarjan. Augmentation problems. SIAM Journal on Computing, 5(4):653–665, 1976.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    G. N. Frederickson and J. Jájá. Approximation algorithms for several graph augmentation problems. SIAM Journal on Computing, 10(2):270–283, 1981.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    H. N. Gabow, Z. Galil, T. Spencer, and R. E. Tarjan. Efficient algorithms for finding minimum spanning trees in undirected and directed graphs. Combinatorica, 6(2):109–122, 1986.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    T.-S. Hsu and V. Ramachandran. On finding a minimum augmentation to biconnect a graph. SIAM Journal on Computing, pages 889–912, 1993.Google Scholar
  5. 5.
    S. Khuller and R. Thurimella. Approximation algorithms for graph augmentation. Journal of Algorithms, 14(2):214–225, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    I. Ljubić and J. Kratica. A genetic algorithm for the biconnectivity augmentation problem. In C. Fonseca, J.-H. Kim, and A. Smith, editors, Proceedings of the 2000 IEEE Congress on Evolutionary Computation, pages 89–96. IEEE Press, 2000.Google Scholar
  7. 7.
    I. Ljubić and G. R. Raidl. An evolutionary algorithm with hill-climbing for the edge-biconnectivity augmentation problem. In E. J. Boers, S. Cagnoni, J. Gottlieb, E. Hart, P. L. Lanzi, G. R. Raidl, R. E. Smith, and H. Tijink, editors, Applications of Evolutionary Computation, volume 2037 of LNCS, pages 20–29. Springer, 2001.CrossRefGoogle Scholar
  8. 8.
    P. Moscato. Memetic algorithms: A short introduction. In D. Corne et al., editors, New Ideas in Optimization, pages 219–234. McGraw Hill, 1999.Google Scholar
  9. 9.
    G. R. Raidl and I. Ljubić. Evolutionary local search for the edge-biconnectivity augmentation problem. to appear in Information Processing Letters, 2001.Google Scholar
  10. 10.
    A. Zhu, S. Khuller, and B. Raghavachari. A uniform framework for approximating weighted connectivity problems. In Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms, pages 937–938, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Sandor Kersting
    • 1
  • Günther R. Raidl
    • 1
  • Ivana Ljubić
    • 1
  1. 1.Institute of Computer Graphics and AlgorithmsVienna University of TechnologyViennaAustria

Personalised recommendations