Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T13:16:45.745Z Has data issue: false hasContentIssue false
  • English
  • Français

On the probable behaviour of some algorithms for finding the stability number of a graph

Published online by Cambridge University Press:  24 October 2008

B. Pittel
B. Pittel
Affiliation:
Ohio State University, Columbus
Get access Rights & Permissions [Opens in a new window]

Abstract

A class of f-driven algorithms due to Chvátal for finding the stability number of a graph are studied. It is shown that, for almost all graphs, the computation time grows subexponentially with n, the number of vertices. If, however, each edge exists with probability δ/n independently on other edges then asymptotically almost certainly the computation time is exponential. Still, for all large enough δ's, these algorithms perform noticeably better than a naive algorithm. The results are extended to random graphs with a fixed number of edges.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 3 , November 1982 , pp. 511 - 526
Copyright
Copyright © Cambridge Philosophical Society 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bollobás, B. and Erdös, P.Cliques in random graphs. Math. Proc. Cambridge Phil. Soc. 80 (1976), 419–427.CrossRefGoogle Scholar
(2)Breiman, L.Probability (Addison-Wesley, Reading, MA, 1968).Google Scholar
(3)Chvátal, V.Determining the stability number of a graph. SIAM J. Comput. 6 (1977), 643–662.Google Scholar
(4)Erdös, P. and Rényi, A.On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5 A (1960), 17–61.Google Scholar
(5)Erdös, P. and Spencer, J.Probabilistic methods in combinatorics. (Academic Press, New York, 1974).Google Scholar
(6)Grimmet, G. R. and Mcdiarmid, C. J. H.On colouring random graphs. Math. Proc. Cambridge Phil. Soc. 77 (1975), 313–324.CrossRefGoogle Scholar
(7)Grimmet, G. R. Random graph theorems. Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the Eighth European Meeting of Statisticians, Tech. Univ. Prague, 1974, vol. A (1977), 203–209.Google Scholar
(8)Lifschitz, V. and Pittel, B.The worst and the most probable performance of a class of set covering algorithms. SIAM J. Comput. (to appear).Google Scholar
(9)Matula, D. W.On the complete subgraphs of a random graph. Proc. 2nd Conf. Combinatorial Theory and Appl., Chapel Hill, NC (1970), pp. 356–369.Google Scholar
(10)McDiarmid, C.Determining the chromatic number of a graph. SIAM J. Comput. 8 (1979), 1–14.CrossRefGoogle Scholar
(11)Tarjan, R. E. and Trojanowski, A. E.Finding a maximum independent set. SIAM J. Comput. 6 (1977), 537–546.Google Scholar