Skip to main content
SpringerLink
Log in

Evolutionary Algorithms and the Maximum Matching Problem

  • Conference paper
  • First Online:
STACS 2003 (STACS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2607))

Included in the following conference series:

Abstract

Randomized search heuristics like evolutionary algorithms are mostly applied to problems whose structure is not completely known but also to combinatorial optimization problems. Practitioners report surprising successes but almost no results with theoretically well-founded analyses exist. Such an analysis is started in this paper for a fundamental evolutionary algorithm and the well-known maximum matching problem. It is proven that the evolutionary algorithm is a polynomial-time randomized approximation scheme (PRAS) for this optimization problem, although the algorithm does not employ the idea of augmenting paths. Moreover, for very simple graphs it is proved that the expected optimization time of the algorithm is polynomially bounded and bipartite graphs are constructed where this time grows exponentially.

Supported in part by the Deutsche Forschungsgemeinschaft (DFG) as part of the Collaborative Research Center “Computational Intelligence” (SFB 531).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. Blum. A simplified realization of the Hopcroft-Karp approach to maximum matching in general graphs. Technical report, Universität Bonn, 1999.

    Google Scholar 

  2. S. Droste, T. Jansen, and I. Wegener. On the optimization of unimodal functions with the (1+1) evolutionary algorithm. In Proc. of the 5th Conf. on Parallel Problem Solving from Nature (PPSN V), LNCS 1498, pages 13–22, 1998.

    Google Scholar 

  3. S. Droste, T. Jansen, and I. Wegener. On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science, 276:51–82, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  4. W. Feller. An Introduction to Probability Theory and Its Applications. Wiley, 1971.

    Google Scholar 

  5. O. Giel and I. Wegener. Evolutionary algorithms and the maximum matching problem. Technical Report CI 142/02, Universität Dortmund, SFB 531, 2002. http://ls2-www.cs.uni-dortmund.de/~wegener/papers/Matchings.ps.

  6. B. Hajek. Hitting-time and occupation-time bounds implied by drift analysis with applications. Advances in Applied Probability, 14:502–525, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. He and X. Yao. Drift analysis and average time complexity of evolutionary algorithms. Artificial Intelligence, 127:57–85, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. E. Hopcroft and R. M. Karp. An n5/2 algorithm for maximum matchings in bipartite graphs. SIAM Journal on Computing, 2(4):225–231, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  9. T. Jansen and I. Wegener. Real royal road functions-where crossover provably is essential. In Proc. of the 3rd Genetic and Evolutionary Computation Conference (GECCO 2001), pages 375–382, 2001.

    Google Scholar 

  10. T. Jansen and I. Wegener. The analysis of evolutionary algorithms-a proof that crossover really can help. Algorithmica, 34:47–66, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  11. S. Micali and V. V. Vazirani. An O(√V. E) algorithm for finding maximum matching in general graphs. In Proc. 21st Annual Symp. on Foundations of Computer Science (FOCS), pages 17–27, 1980.

    Google Scholar 

  12. G. H. Sasaki and B. Hajek. The time complexity of maximum matching by simulated annealing. Journal of the ACM, 35:387–403, 1988.

    Article  MathSciNet  Google Scholar 

  13. J. Scharnow, K. Tinnefeld, and I. Wegener. Fitness landscapes based on sorting and shortest paths problems. In Proc. of the 7th Conf. on Parallel Problem Solving from Nature (PPSN VII), LNCS 2439, pages 54–63, 2002.

    Google Scholar 

  14. V. V. Vazirani. A theory of alternating paths and blossoms for proving correctness of the O(√V E) maximum matching algorithm. Combinatorica, 14(1):71–109, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  15. I. Wegener. Theoretical aspects of evolutionary algorithms. In Proc. of the 28th Internat. Colloq. on Automata, Languages and Programming (ICALP), LNCS 2076, pages 64–78, 2001.

    Google Scholar 

  16. I. Wegener and C. Witt. On the analysis of a simple evolutionary algorithm on quadratic pseudo-boolean functions. Journal of Discrete Algorithms, 2002. To appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FB Informatik, Univ. Dortmund, LS 2, 44221, Dortmund, Germany

    Oliver Giel & Ingo Wegener

Authors
  1. Oliver Giel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ingo Wegener
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takusstr. 9, 14195, Berlin, Germany

    Helmut Alt

  2. LIRMM, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Michel Habib

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Giel, O., Wegener, I. (2003). Evolutionary Algorithms and the Maximum Matching Problem. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_37

Download citation

  • DOI: https://doi.org/10.1007/3-540-36494-3_37

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation