Skip to main content

Engineering Algorithms for Approximate Weighted Matching

  • Conference paper
Experimental Algorithms (WEA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4525))

Included in the following conference series:

Abstract

We present a systematic study of approximation algorithms for the maximum weight matching problem. This includes a new algorithm which provides the simple greedy method with a recent path heuristic. Surprisingly, this quite simple algorithm performs very well, both in terms of running time and solution quality, and, though some other methods have a better theoretical performance, it ranks among the best algorithms.

Part of this work was done at Max-Planck-Institut für Informatik, Saarbrücken, Germany. Partially supported by DFG grants SA 933/1-2, SA 933/1-3.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

  • Edmonds, J.: Maximum matching and a polyhedron with 0,1-vertices. J. Res. Nat. Bur. Standards 69B, 125–130 (1965)

    MathSciNet  Google Scholar 

  • Gabow, H.N.: Data structures for weighted matching and nearest common ancestors with linking. In: Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-90), SIAM, pp. 434–443 (1990)

    Google Scholar 

  • Gabow, H.N., Tarjan, R.E.: Faster scaling algorithms for general graph matching problems. Journal of the ACM 38, 815–853 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  • Lipton, R.J., Tarjan, R.E.: Applications of a planar separator theorem. SIAM Journal on Computing 9, 615–627 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  • Micali, S., Vazirani, V.V.: An \(\mathcal{O}(\sqrt{|V|}|{E}|)\) algorithm for finding maximum matching in general graphs. In: Proceedings of the 21st Annual Symposium on Foundations of Computer Science (FOCS-80), pp. 17–27. IEEE Press, New York (1980)

    Google Scholar 

  • Vazirani, V.V.: A theory of alternating paths and blossoms for proving correctness of the \(\mathcal{O}(\sqrt{V}{E})\) general graph maximum matching algorithm. Combinatorica 14, 71–109 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  • Mehlhorn, K., Schäfer, G.: Implementation of O(nm log n) weighted matchings in general graphs: The power of data structures. ACM Journal of Experimental Algorithms, 7 (2002)

    Google Scholar 

  • Galil, Z., Micali, S., Gabow, H.N.: An O(EVlogV) algorithm for finding a maximal weighted matching in general graphs. SIAM Journal on Computing 15, 120–130 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • Cook, W., Rohe, A.: Computing minimum-weight perfect matchings. INFORMS Journal on Computing 11, 138–148 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • Drake Vinkemeier, D.E., Hougardy, S.: A linear-time approximation algorithm for weighted matchings in graphs. ACM Trans. Algorithms 1, 107–122 (2005)

    Article  MathSciNet  Google Scholar 

  • Avis, D.: A survey of heuristics for the weighted matching problem. Networks 13, 475–493 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  • Preis, R.: Linear time 1/2-approximation algorithm for maximum weighted matching in general graphs. In: Meinel, C., Tison, S. (eds.) STACS 99. LNCS, vol. 1563, pp. 259–269. Springer, Heidelberg (1999)

    Google Scholar 

  • Drake, D.E., Hougardy, S.: A simple approximation algorithm for the weighted matching problem. Information Processing Letters 85, 211–213 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Drake, D.E., Hougardy, S.: Linear time local improvements for weighted matchings in graphs. In: Jansen, K., Margraf, M., Mastrolli, M., Rolim, J.D.P. (eds.) WEA 2003. LNCS, vol. 2647, pp. 107–119. Springer, Heidelberg (2003)

    Google Scholar 

  • Pettie, S., Sanders, P.: A simpler linear time 2/3 − ε approximation for maximum weight matching. Information Processing Letters 91, 271–276 (2004)

    Article  MathSciNet  Google Scholar 

  • Mehlhorn, K., Näher, S.: LEDA - A Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  • Soper, A.J., Walshaw, C., Cross, M.: A combined evolutionary search and multilevel optimisation approach to graph-partitioning. J. Global Optimization 29, 225–241 (2004), http://staffweb.cms.gre.ac.uk/~c.walshaw/partition/

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Camil Demetrescu

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Maue, J., Sanders, P. (2007). Engineering Algorithms for Approximate Weighted Matching . In: Demetrescu, C. (eds) Experimental Algorithms. WEA 2007. Lecture Notes in Computer Science, vol 4525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72845-0_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72845-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72844-3

  • Online ISBN: 978-3-540-72845-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics