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Improved Guarantees for Tree Cut Sparsifiers

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Algorithms - ESA 2014 (ESA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8737))

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Abstract

Harrelson, Hildrum and Rao [11] construct for a given graph a single tree that acts as a flow sparsifier, i.e., it can approximate multicommodity flows in G up to an O(log 2 nloglog n) factor. Many applications that use these trees do not actually require a flow sparsifier but would already work with just having a cut sparsifier. We show how to construct a cut sparsifier that is a single tree and has quality O(log 1.5 nloglog n).

In addition we show a close connection of this problem to the Mincut Linear Arrangement Problem which shows that improving the guarantee to o(log 1.5 n) might be difficult.

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Germany

    Harald Räcke & Chintan Shah

Authors
  1. Harald Räcke
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  2. Chintan Shah
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Editor information

Editors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, USA

    Andreas S. Schulz

  2. Karlsruhe Institute of Technology (KIT), Kaiserstruhe 12, 76131, Karlsruhe, Germany

    Dorothea Wagner

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Räcke, H., Shah, C. (2014). Improved Guarantees for Tree Cut Sparsifiers. In: Schulz, A.S., Wagner, D. (eds) Algorithms - ESA 2014. ESA 2014. Lecture Notes in Computer Science, vol 8737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44777-2_64

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  • DOI: https://doi.org/10.1007/978-3-662-44777-2_64

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44776-5

  • Online ISBN: 978-3-662-44777-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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