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A Nondifferentiable Optimization Approach to Ratio-Cut Partitioning

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Experimental and Efficient Algorithms (WEA 2003)

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Abstract

We propose a new method for finding the minimum ratio-cut of a graph. Ratio-cut is NP-hard problem for which the best previously known algorithm gives an O(log n)-factor approximation by solving its dually related maximum concurrent flow problem. We formulate the minimum ratio-cut as a certain nondifferentiable optimization problem, and show that the global minimum of the optimization problem is equal to the minimum ratio-cut. Moreover, we provide strong symbolic computation based evidence that any strict local minimum gives an approximation by a factor of 2. We also give an efficient heuristic algorithm for finding a local minimum of the proposed optimization problem based on standard nondifferentiable optimization methods and evaluate its performance on several families of graphs. We achieve O(n 1.6) experimentally obtained running time on these graphs.

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, University of Latvia, Raina blvd. 29, LV-1459, Riga, Latvia

    Kārlis Freivalds

Authors
  1. Kārlis Freivalds
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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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Freivalds, K. (2003). A Nondifferentiable Optimization Approach to Ratio-Cut Partitioning. 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_11

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  • DOI: https://doi.org/10.1007/3-540-44867-5_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40205-3

  • Online ISBN: 978-3-540-44867-9

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