An Improved Integrality Gap for the Călinescu-Karloff-Rabani Relaxation for Multiway Cut

  • Haris Angelidakis
  • Yury Makarychev
  • Pasin Manurangsi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10328)

Abstract

We construct an improved integrality gap instance for the Călinescu-Karloff-Rabani LP relaxation of the Multiway Cut problem. For \(k \geqslant 3\) terminals, our instance has an integrality ratio of \(6 / (5 + \frac{1}{k - 1}) - \varepsilon \), for every constant \(\varepsilon > 0\). For every \(k \geqslant 4\), this improves upon a long-standing lower bound of \(8 / (7 + \frac{1}{k - 1})\) by Freund and Karloff [7]. Due to the result by Manokaran et al. [9], our integrality gap also implies Unique Games hardness of approximating Multiway Cut of the same ratio.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Haris Angelidakis
    • 1
  • Yury Makarychev
    • 1
  • Pasin Manurangsi
    • 2
  1. 1.Toyota Technological Institute at ChicagoChicagoUSA
  2. 2.University of California, BerkeleyBerkeleyUSA

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