Improved Guarantees for Tree Cut Sparsifiers

  • Harald Räcke
  • Chintan Shah
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8737)

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(log2nloglogn) 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(log1.5nloglogn).

In addition we show a close connection of this problem to the Mincut Linear Arrangement Problem which shows that improving the guarantee to o(log1.5n) might be difficult.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Harald Räcke
    • 1
  • Chintan Shah
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenGermany

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