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A Flow-Based Method for Improving the Expansion or Conductance of Graph Cuts

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Integer Programming and Combinatorial Optimization (IPCO 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3064))

Abstract

We discuss the Max-flow Quotient-cut Improvement (MQI) algorithm, a flow-based method for improving graph cuts when cut quality is measured by quotient-style metrics such as expansion or conductance. Given a cut \((S,\overline{S})\), this algorithm finds the best improvement among all cuts \((S',\overline{S'})\) such that S′ is a strict subset of S. This idea has already been used by theorists to give improved bounds for graph bisection and for finding hierarchical oblivous routing schemes. Here we investigate the practical utility of the idea and find that MQI can be combined with Metis to obtain a heuristic graph partitioner that does an extremely good job on classic benchmark graphs, VLSI circuits, and four different tasks from the Information Retrieval domain. We also find empirically that Metis+MQI runs in nearly linear time, so it is applicable to very large problems.

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Author information

Authors and Affiliations

  1. Yahoo, 210 S. Delacey Ave No.105, Pasadena, CA, 91105, USA

    Kevin Lang

  2. CS Dept, Soda Hall UCB, Berkeley, CA, 94720, USA

    Satish Rao

Authors
  1. Kevin Lang
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  2. Satish Rao
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Editors and Affiliations

  1. Department of IEOR, Columbia University, 500 West 120th Street, 10027, New York, NY, USA

    Daniel Bienstock

  2. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    George Nemhauser

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© 2004 Springer-Verlag Berlin Heidelberg

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Lang, K., Rao, S. (2004). A Flow-Based Method for Improving the Expansion or Conductance of Graph Cuts. In: Bienstock, D., Nemhauser, G. (eds) Integer Programming and Combinatorial Optimization. IPCO 2004. Lecture Notes in Computer Science, vol 3064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25960-2_25

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  • DOI: https://doi.org/10.1007/978-3-540-25960-2_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22113-5

  • Online ISBN: 978-3-540-25960-2

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