Minimum Birkhoff-von Neumann Decomposition

  • Janardhan Kulkarni
  • Euiwoong Lee
  • Mohit SinghEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10328)


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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Microsoft ResearchRedmondUSA
  2. 2.Carnegie Mellon UniversityPittsburghUSA
  3. 3.Georgia Institute of TechnologyAtlantaUSA

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