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International Workshop on Experimental and Efficient Algorithms

WEA 2003: Experimental and Efficient Algorithms pp 107–119Cite as

Linear Time Local Improvements for Weighted Matchings in Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2647))

Abstract

Recently two different linear time approximation algorithms for the weighted matching problem in graphs have been suggested [5][17]. Both these algorithms have a performance ratio of 1/2. In this paper we present a set of local improvement operations and prove that it guarantees a performance ratio of 2/3. We show that a maximal set of these local improvements can be found in linear time.

To see how these local improvements behave in practice we conduct an experimental comparison of four different approximation algorithms for calculating maximum weight matchings in weighted graphs. One of these algorithms is the commonly used Greedy algorithm which achieves a performance ratio of 1/2 but has O(m log n) runtime. The other three algorithms all have linear runtime. Two of them are the above mentioned 1/2 approximation algorithms. The third algorithm may have an arbitrarily bad performance ratio but in practice produces reasonably good results. We compare the quality of the algorithms on a test set of weighted graphs and study the improvement achieved by our local improvement operations. We also do a comparison of the runtimes of all algorithms.

Supported by DFG research grant 296/6-3

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Author information

Authors and Affiliations

  1. Institut für Informatik, Humboldt-Universität zu Berlin, 10099, Berlin, Germany

    Doratha E. Drake & Stefan Hougardy

Authors
  1. Doratha E. Drake
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  2. Stefan Hougardy
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Editor information

Editors and Affiliations

  1. Institute of Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen  & Marian Margraf  & 

  2. IDISIA - Instituto Dalle Molle di Studi sull’Intelligenza Artificiale, Galleria 2, 6928, Manno, Switzerland

    Monaldo Mastrolilli

  3. Université de Genève 4, Switzerland

    José D. P. Rolim

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© 2003 Springer-Verlag Berlin Heidelberg

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Drake, D.E., Hougardy, S. (2003). Linear Time Local Improvements for Weighted Matchings in Graphs. In: Jansen, K., Margraf, M., Mastrolilli, M., Rolim, J.D.P. (eds) Experimental and Efficient Algorithms. WEA 2003. Lecture Notes in Computer Science, vol 2647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44867-5_9

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  • DOI: https://doi.org/10.1007/3-540-44867-5_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40205-3

  • Online ISBN: 978-3-540-44867-9

  • eBook Packages: Springer Book Archive

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