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Minimum Birkhoff-von Neumann Decomposition

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Integer Programming and Combinatorial Optimization (IPCO 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10328))

Abstract

Motivated by the applications in routing in data centers, we study the problem of expressing an \(n \times n\) doubly stochastic matrix as a linear combination using the smallest number of (sub)permutation matrices. The Birkhoff-von Neumann decomposition theorem proves that there exists such a decomposition, but does not give a representation with the smallest number of permutation matrices. In particular, we consider the case when the optimal decomposition uses a constant number of matrices. We show that the problem is not fixed parameter tractable, and design a logarithmic approximation to the problem.

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Authors and Affiliations

  1. Microsoft Research, Redmond, USA

    Janardhan Kulkarni

  2. Carnegie Mellon University, Pittsburgh, USA

    Euiwoong Lee

  3. Georgia Institute of Technology, Atlanta, USA

    Mohit Singh

Authors
  1. Janardhan Kulkarni
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  2. Euiwoong Lee
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  3. Mohit Singh
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Corresponding author

Correspondence to Mohit Singh .

Editor information

Editors and Affiliations

  1. Ecole Polytechnique Federale de Lausanne - EPFL, Lausanne, Switzerland

    Friedrich Eisenbrand

  2. University of Waterloo, Waterloo, Ontario, Canada

    Jochen Koenemann

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Kulkarni, J., Lee, E., Singh, M. (2017). Minimum Birkhoff-von Neumann Decomposition. In: Eisenbrand, F., Koenemann, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2017. Lecture Notes in Computer Science(), vol 10328. Springer, Cham. https://doi.org/10.1007/978-3-319-59250-3_28

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  • DOI: https://doi.org/10.1007/978-3-319-59250-3_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59249-7

  • Online ISBN: 978-3-319-59250-3

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