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Linear Time 1/2-Approximation Algorithm for Maximum Weighted Matching in General Graphs

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STACS 99 (STACS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1563))

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Abstract

A new approximation algorithm for maximum weighted matching in general edge-weighted graphs is presented. It calculates a matching with an edge weight of at least 1/2 of the edge weight of a maximum weighted matching. Its time complexity is O(|E|), with |E| being the number of edges in the graph. This improves over the previously known 1/2-approximation algorithms for maximum weighted matching which require O(|E|· log(|V|)) steps, where |V| is the number of vertices.

Supported by DFG/HNI-Graduiertenkolleg ”Parallele Rechnernetze in der Produktionstechnik” and DFG Sonderforschungsbereich 376: ”Massive Parallelität”

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. B. Boyens. Schrumpfungstechniken zur effizienten Graphpartitionierung. Diplom-Thesis, Universität Paderborn, Germany, June 1998. (in German).

    Google Scholar 

  3. H.N. Gabow. Data structures for weighted matching and nearest common ancestors with linking. ACM-SIAM Symposium on Discrete Algorithms., pages 434–443, 1990.

    Google Scholar 

  4. H.N. Gabow and R.E. Tarjan. Faster scaling algorithms for general graph-matching problems. Journal of the ACM, 38(4):815–853, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  5. M.R. Garey, D.S. Johnson, and L. Stockmeyer. Some simplified NP-complete graph problems. Theoretical Computer Science, 1:237–267, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Hopcroft and R.M. Karp. An O(n 5/2) algorithm for maximum matching in bipartite graphs. SIAM Journal on Computing, 2:225–231, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Karpinski and W. Rytter. Fast Parallel Algorithms for Graph Matching Problems, Oxford Lecture Series in Math. and its Appl.. Oxford University Press, 1998.

    Google Scholar 

  8. E.L. Lawler. Combinatorial Optimization: Networks and Matroids. Holt, Rinehart and Winston, New York, 1976.

    MATH  Google Scholar 

  9. L. Lovász and M.D. Plummer. Matching Theory, volume 29 of Annals of Discrete Mathematics. North-Holland Mathematics Studies, 1986.

    Google Scholar 

  10. S. Micali and V.V. Vazirani. An O(√ • E) algorithm for finding maximum matching in general graphs. In IEEE Annual Symposium on Foundations of Computer Science, pages 17–27, 1980.

    Google Scholar 

  11. R. Preis and R. Diekmann. The PARTY partitioning-library, user guide, version 1.1. Technical Report TR-RSFB-96-024, Universität Paderborn, Sep 1996.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Universität Paderborn, D-33095, Paderborn, Germany

    Robert Preis

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  1. Robert Preis
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Editors and Affiliations

  1. FB IV - Informatik, Universität Trier, D-54286, Trier, Germany

    Christoph Meinel

  2. LIFL, Université de Lille I, Bătiment 3, F-59655, Villeneuve d’Ascq Cedex, France

    Sophie Tison

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© 1999 Springer-Verlag Berlin Heidelberg

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Preis, R. (1999). Linear Time 1/2-Approximation Algorithm for Maximum Weighted Matching in General Graphs. In: Meinel, C., Tison, S. (eds) STACS 99. STACS 1999. Lecture Notes in Computer Science, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49116-3_24

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  • DOI: https://doi.org/10.1007/3-540-49116-3_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65691-3

  • Online ISBN: 978-3-540-49116-3

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