Advertisement

Algorithmica

, Volume 3, Issue 1–4, pp 511–533 | Cite as

The general maximum matching algorithm of micali and vazirani

  • Paul A. Peterson
  • Michael C. Loui
Article

Abstract

We give a clear exposition of the algorithm of Micali and Vazirani for computing a maximum matching in a general graph. This is the most efficient algorithm known for general matching. On a graph withn vertices andm edges this algorithm runs inO(n 1/2 m) time.

Key words

Matching Graph algorithm Combinatorial optimization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aho, A. V., Hopcroft, J. E., and Ullman, J. D. (1974),The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA.zbMATHGoogle Scholar
  2. Berge, C. (1957), Two theorems in graph theory,Proc. Nat. Acad. Sci. U.S.A. 43, 842–844.zbMATHCrossRefMathSciNetGoogle Scholar
  3. Bondy, J. A., and Murty, U. S. R. (1976),Graph Theory with Applications, Elsevier North-Holland, New York.Google Scholar
  4. Edmonds, J. (1965), Paths, trees and flowers,Canad. J. Math. 17, 449–467.zbMATHMathSciNetGoogle Scholar
  5. Even, S., and Kariv, O. (1975), AnO(n 2.5) algorithm for maximum matching in general graphs,Proc. 16th Ann. Symp. on Foundations of Computer Science, IEEE, pp. 100–112.Google Scholar
  6. Fujii, M., Kasami, T., and Ninomiya, K. (1969), Optimal sequencing of two equivalent processors,SIAM J. Appl. Math. 17, 784–789.zbMATHCrossRefMathSciNetGoogle Scholar
  7. Gabow, H. N. (1976), An efficient implementation of Edmonds' algorithm for maximum matching on graphs,J. Assoc. Comput. Mach. 23, 221–234.zbMATHMathSciNetGoogle Scholar
  8. Gabow, H. N., and Tarjan, R. E. (1985), A linear-time algorithm for a special case of disjoint set union,J. Comput. System Sci. 30, 209–221.zbMATHCrossRefMathSciNetGoogle Scholar
  9. Hajek, B. (1984), Link schedules, flows, and the multichromatic index of graphs,Proc. 1984 Conf. on Information Sciences and Systems, Princeton University, Princeton, NJ, pp. 498–502.Google Scholar
  10. Hopcroft, J. E., and Karp, R. M. (1973), Ann 5/2 algorithm for maximum matching in bipartite graphs,SIAM J. Comput. 2, 225–231.zbMATHCrossRefMathSciNetGoogle Scholar
  11. Kameda, T., and Munro, I. (1974), AnO(¦V¦ · ¦E¦) algorithm for maximum matching of graphs,Computing 12, 91–98.zbMATHCrossRefMathSciNetGoogle Scholar
  12. Micali, S., and Vazirani, V. (1980), An O(√¦v∥E¦) algorithm for finding maximum matching in general graphs,Proc. 21st Ann. Symp. on Foundations of Computer Science, IEEE, pp. 17–27.Google Scholar
  13. Papadimitriou, C. H., and Steiglitz, K. (1982),Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, Englewood Cliffs, NJ.zbMATHGoogle Scholar
  14. Peterson, P. A. (1985), The general maximum matching algorithm of Micali and Vazirani, Tech. Rep. ACT-62, Coordinated Sci. Lab., Univ. Illinois at Urbana-Champaign, Aug. 1985.Google Scholar
  15. Reingold, E. M., Nievergelt, J., and Deo, N. (1977),Combinatorial Algorithms: Theory and Practice, Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  16. Tarjan, R. E. (1975), Efficiency of a good but not linear set union algorithm,J. Assoc. Comput. Mach. 22, 215–225.zbMATHMathSciNetGoogle Scholar
  17. Tarjan, R. E. (1983),Data Structures and Network Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Paul A. Peterson
    • 1
  • Michael C. Loui
    • 1
  1. 1.Department of Electrical and Computer Engineering and Coordinated Science LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Personalised recommendations