Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

STABULUS: A technique for finding stable sets in large graphs with tabu search

STABULUS: Eine Technik zur Bestimmung unabhängiger Knotenmengen in großen Graphen mit der Tabu-Search-Methode

Abstract

Numerical experiments with tabu search have been carried out for constructing independent sets in large graphs. We present some variations on the independent set problem and discuss the results obtained by the tabu search technique.

As for graph coloring, this method seems to be a very efficient heuristic procedure.

Zusammenfassung

Numerische Experimente mit der sogenannten Tabu-Search-Methode wurden durchgeführt, um unabhängige Knotenmengen in Graphen zu finden (eine KnotenmengeS ist dann unabhängig, wenn keine Kante beide Endknoten inS hat).

Einige Variationen über dieses Problem werden betrachtet (eine gewichtete Version wird beschrieben) und wir geben Resultate an, die zeigen, daß die Tabu-Methode für die Bestimmung unabhängiger Knotenmengen so effizient wie für die Graphenfärbung ist.

This is a preview of subscription content, log in to check access.

References

  1. [1]

    Balas, E., Yu, C.: Finding a maximum clique in an arbitrary graph. SIAM J. Comput.15, 1054–1068 (1986).

  2. [2]

    Berge, C.: Graphes. Paris: Gauthier-Villars 1983.

  3. [3]

    Bollobàs, B., Thomason, A.: Random graphs of small order, Random graphs '83. Annals of Discrete Mathematics28, 47–97 (1985).

  4. [4]

    Chams, M., Hertz, A., de Werra, D.: Some experiments with simulated annealing for coloring graphs. European Journal of Operational Research32, 260–266 (1987).

  5. [5]

    Glover, F.: Tabu search. Paper presented at ORSA/TIMS meeting, St. Louis, Mo (1987).

  6. [6]

    Glover, F.: Future paths for integer programming and links to artificial intelligence. Computers and Operations Research13, 533–549 (1986).

  7. [7]

    Hertz, A., de Werra, D.: Using tabu search techniques for graph coloring. Computing39, 345–351 (1987).

  8. [8]

    Johnson, D. S., Yannakakis, M., Papadimitriou, C. H.: On generating all maximal independent sets. Information Processing Letters27, 119–123 (1988).

  9. [9]

    Johri, A., Matula, D. W.: Probabilistic bounds and heuristic algorithms for coloring large random graphs. Southern Methodist University, Dallas, Texas (1982).

  10. [10]

    Leighton, F.: A graph coloring algorithm for large scheduling problems. Journal of Research of the National Bureau of Standards84, 489–503 (1979).

  11. [11]

    Loukakis, E.: A new backtracking algorithm for generating the family of maximal independent sets of a graph. Computer and Mathematics with Applications9, 583–589 (1983).

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Friden, C., Hertz, A. & de Werra, D. STABULUS: A technique for finding stable sets in large graphs with tabu search. Computing 42, 35–44 (1989). https://doi.org/10.1007/BF02243141

Download citation

Key words

  • Independent set
  • tabu search
  • heuristic procedure
  • timetabling