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European Symposium on Algorithms

ESA 2003: Algorithms - ESA 2003 pp 752–764Cite as

Multicommodity Flow Approximation Used for Exact Graph Partitioning

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2832))

Abstract

We present a fully polynomial-time approximation scheme for a multicommodity flow problem that yields lower bounds of the graph bisection problem. We compare the approximation algorithm with Lagrangian relaxation based cost-decomposition approaches and linear programming software when embedded in an exact branch&bound approach for graph bisection. It is shown that the approximation algorithm is clearly superior in this context. Furthermore, we present a new practical addition to the approximation algorithm which improves its performance distinctly. Finally, we prove the performance of the graph bisection algorithm using multicommodity flow approximation by computing formerly unknown bisection widths of some DeBruijn- and Shuffle-Exchange-Graphs.

This work was partly supported by the German Science Foundation (DFG) project SFB-376, by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT), and by the Intelligent Information Systems Institute, Cornell University (AFOSR grant F49620-01-1-0076.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Cornell University, 4130 Upson Hall, Ithaca, NY, 14853, U.S.A.

    Meinolf Sellmann

  2. Faculty of Computer Science, Electrical Engineering, and Mathematics, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Norbert Sensen & Larissa Timajev

Authors
  1. Meinolf Sellmann
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  2. Norbert Sensen
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  3. Larissa Timajev
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica e Automazione, Università degli Studi “Roma Tre”, via della Vasca Navale 79, 00146, Rome, Italy

    Giuseppe Di Battista

  2. School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Uri Zwick

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Sellmann, M., Sensen, N., Timajev, L. (2003). Multicommodity Flow Approximation Used for Exact Graph Partitioning. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_67

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  • DOI: https://doi.org/10.1007/978-3-540-39658-1_67

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20064-2

  • Online ISBN: 978-3-540-39658-1

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