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Between Min Cut and Graph Bisection

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Mathematical Foundations of Computer Science 1993 (MFCS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 711))

Abstract

We investigate a class of graph partitioning problems whose two extreme representatives are the well-known Min Cut and Graph Bisection problems. The former is known to be efficiently solvable by flow techniques, the latter to be NP-complete. The results presented in this paper are

  • a monotony result of the type“ The more balanced the partition we look for has to be, the harder the problem”.

  • a complexity result clarifying the status of a large part of intermediate problems in the class.

Thus we show the existence and partly localize an“ efficiency border” between the two extremes.

This work was done while the authors were with Lehrstuhl für angewandte Mathematik insbesondere Informatik, Rheinisch-Westfälische Technische Hochschule Aachen.

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References

  1. T. N. Bui, S. Chaudhuri, F. T. Leighton, M. Sipser: Graph Bisection Algorithms With Good Average Case Behaviour, Combinatorica 7 (1987) 171–191

    Google Scholar 

  2. L. R. Ford, D. R. Fulkerson: Maximal Flow Through a Network, Canadian J. Math. 8 (1956) 399–404

    Google Scholar 

  3. M. J. Garey, D. S. Johnson, L. Stockmeyer: Some Simplified NP-complete Graph Problems, Theoretical Computer Science 1 (1976) 237–267

    Google Scholar 

  4. A. V. Goldberg, R. E. Tarjan: A New Approach to the Maximum Flow Problem, Journal of the ACM 35 (1988) 921–940

    Google Scholar 

  5. J. Hao, J. B. Orlin: A Faster Algorithm for Finding the Minimum Cut in a Graph, Proceedings of the third ACM-SIAM Symposium on Discrete Algorithms (SODA'91) (1991) 165–174

    Google Scholar 

  6. R. J. Lipton, R. E. Tarjan: A Planar Separator Theorem, SIAM J. on Applied Math. 36 (1979) 177–189

    Google Scholar 

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, W-1000, Berlin 12, Germany

    Dorothea Wagner

  2. Institut für Informatik. Fachbereich Mathematik, Freie Universität Berlin, Arnimallee 2-6, W-1000, Berlin 33, Germany

    Frank Wagner

Authors
  1. Dorothea Wagner
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  2. Frank Wagner
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Editor information

Andrzej M. Borzyszkowski Stefan Sokołowski

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© 1993 Springer-Verlag Berlin Heidelberg

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Wagner, D., Wagner, F. (1993). Between Min Cut and Graph Bisection. In: Borzyszkowski, A.M., Sokołowski, S. (eds) Mathematical Foundations of Computer Science 1993. MFCS 1993. Lecture Notes in Computer Science, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57182-5_65

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  • DOI: https://doi.org/10.1007/3-540-57182-5_65

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57182-7

  • Online ISBN: 978-3-540-47927-7

  • eBook Packages: Springer Book Archive

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