Engineering Algorithms for Approximate Weighted Matching

  • Jens Maue
  • Peter Sanders
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4525)

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Edmonds, J.: Maximum matching and a polyhedron with 0,1-vertices. J. Res. Nat. Bur. Standards 69B, 125–130 (1965)MathSciNetGoogle Scholar
  2. 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
  3. Gabow, H.N., Tarjan, R.E.: Faster scaling algorithms for general graph matching problems. Journal of the ACM 38, 815–853 (1991)MATHCrossRefMathSciNetGoogle Scholar
  4. Lipton, R.J., Tarjan, R.E.: Applications of a planar separator theorem. SIAM Journal on Computing 9, 615–627 (1980)MATHCrossRefMathSciNetGoogle Scholar
  5. 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
  6. 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)MATHCrossRefMathSciNetGoogle Scholar
  7. 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
  8. 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)MATHCrossRefMathSciNetGoogle Scholar
  9. Cook, W., Rohe, A.: Computing minimum-weight perfect matchings. INFORMS Journal on Computing 11, 138–148 (1999)MATHMathSciNetCrossRefGoogle Scholar
  10. Drake Vinkemeier, D.E., Hougardy, S.: A linear-time approximation algorithm for weighted matchings in graphs. ACM Trans. Algorithms 1, 107–122 (2005)CrossRefMathSciNetGoogle Scholar
  11. Avis, D.: A survey of heuristics for the weighted matching problem. Networks 13, 475–493 (1983)MATHCrossRefMathSciNetGoogle Scholar
  12. 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
  13. Drake, D.E., Hougardy, S.: A simple approximation algorithm for the weighted matching problem. Information Processing Letters 85, 211–213 (2003)CrossRefMathSciNetMATHGoogle Scholar
  14. 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
  15. Pettie, S., Sanders, P.: A simpler linear time 2/3 − ε approximation for maximum weight matching. Information Processing Letters 91, 271–276 (2004)CrossRefMathSciNetGoogle Scholar
  16. Mehlhorn, K., Näher, S.: LEDA - A Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)MATHGoogle Scholar
  17. 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/ MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Jens Maue
    • 1
  • Peter Sanders
    • 2
  1. 1.ETH Zürich, Institute of Theoretical Computer Science, Universitätsstrasse 6, 8092 ZürichSwitzerland
  2. 2.Universität Karlsruhe (TH), Fakultät für Informatik, Postfach 6980, 76128 KarlsruheGermany

Personalised recommendations