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A Unified Framework for Approximating Multiway Partition Problems

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Book cover Algorithms and Computation (ISAAC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2223))

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Abstract

We present a simple and unified framework for developing and analyzing approximation algorithms for some multiway partition problems (with or without terminals), including the k-way cut (or kcut), multiterminal cut (or multiway cut), hypergraph partition and target split.

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References

  1. G. Călinescu, H. Karlo. and Y. Rabani. An Improved Approximation Algorithm for Multiway Cut. In Proc. STOC 1998, pp. 48–52, 1998.

    Google Scholar 

  2. S. Chopra and J. H. Owen. A Note on Formulations for the A-Partition Problem on Hypergraphs. Discrete Applied Mathematics 90, pp. 115–133, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. Dalhaus, D. S. Johnson, C. H. Papadimitriou, P. Seymour and M. Yannakakis. The Complexity of the Multiterminal Cuts. SIAM J. Comput. Vol. 23, No. 4, pp. 864–894, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  4. O. Goldschmidt and D. S. Hochbaum. A Polynomial Algorithm for the k-cut Problem for fixed k. Math. Oper. Res. 19, No. 1, pp. 24–37, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Grötschel, L. Lovasz and A. Schrijver. Geometric Algorithms and Combinatorial Optimization. Springer, Berlin, 1998.

    MATH  Google Scholar 

  6. S. Iwata, L. L. Fleischer and S. Fujishige. A Combinatorial, Strongly Polynomial-Time Algorithm for Minimizing Submodular Functions. In Proc. STOC 2000, pp. 97–106, 2000.

    Google Scholar 

  7. S. Kapoor. On Minimum 3-cuts and Approximating k-cuts Using Cut Trees. IPCO 1996, LNCS 1084, pp. 132–146, 1996.

    Google Scholar 

  8. D. R. Karger, P. Klein, C. Stein, M. Thorup and N. E. Young. Rounding Algorithms for a Geometric Embedding of Minimum Multiway Cut. In Proc. STOC 1999, pp. 668–678, 1999.

    Google Scholar 

  9. D. R. Karger and C. Stein. A New Approach to the Minimum Cut Problems. J. of ACM 43, No. 4, pp. 601–640, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  10. T. Lengauer. Combinatorial Algorithms for Integrated Circuit Layout. Wiley, New York, 1990.

    MATH  Google Scholar 

  11. D. W. Matula, A Linear Time 2 + ∈ Approximation Algorithm for Edge Connectivity. In Proc. SODA 1993, pp. 500–504, 1993.

    Google Scholar 

  12. N. Maeda, H. Nagamochi, T. Ibaraki. Approximate Algorithms for Multiway Objective Point Split Problems of Graphs (Japanese). Computing Devices and Algorithms (Japanese) (Kyoto, 1993). Surikaisekikenkyusho Kokyuroku No. 833, pp. 98–109, 1993.

    Google Scholar 

  13. H. Nagamochi and T. Ibaraki. A Fast Algorithm for Computing Minimum 3-way and 4-way Cuts. Mathematical Programming 88, No. 3, pp. 507–520, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Nagamochi, S. Katayama and T. Ibaraki. A Faster Algorithm for Computing Minimum 5-way and 6-way Cuts in Graphs. J. Combinatorial Optimization 4, pp. 35–78, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  15. H. Narayanan, S. Roy and S. Patkar. Approximation Algorithms for Min-k-Overlap Problems Using the Principal Lattice of Partitions Approach. J. Algorithms 21, pp. 306–330, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  16. M. Queyranne. Minimizing Symmetric Submodular Functions. Mathematical Programming B 82, pp. 3–12, 1998.

    MathSciNet  MATH  Google Scholar 

  17. M. Queyranne. On Optimum Size-Constrained Set Partitions. AUSSOIS 1999, France, March 8–12, 1999.

    Google Scholar 

  18. A. Schrijver. A Combinatorial Algorithm Minimizing Submodular Functions in Strongly Polynomial Time. J. Combin. Theory B 80, No. 2, pp. 346–355, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  19. H. Saran and V. V. Vazirani. Finding k-cuts within Twice the Optimal. SIAM J. Comput. 24, No. 1, pp. 101–108, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  20. L. Zhao, H. Nagamochi and T. Ibaraki. Approximating the Minimum k-way Cut in a Graph via Minimum 3-way Cuts. ISAAC 1999, LNCS 1741, pp. 373–382, 1999. Full paper will appear in J. Combinatorial Optimization.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Kyoto University, Kyoto, Japan

    Liang Zhao & Toshihide Ibaraki

  2. Toyohashi University of Technology, Toyohashi, Japan

    Hiroshi Nagamochi

Authors
  1. Liang Zhao
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  2. Hiroshi Nagamochi
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  3. Toshihide Ibaraki
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Editor information

Editors and Affiliations

  1. Basser Department of Computer Science, University of Sydney, Madsen Building F09, 2006, Sydney, NSW, Australia

    Peter Eades

  2. Department of Computer Science, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    Tadao Takaoka

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© 2001 Springer-Verlag Berlin Heidelberg

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Zhao, L., Nagamochi, H., Ibaraki, T. (2001). A Unified Framework for Approximating Multiway Partition Problems. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_58

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  • DOI: https://doi.org/10.1007/3-540-45678-3_58

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42985-2

  • Online ISBN: 978-3-540-45678-0

  • eBook Packages: Springer Book Archive

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