computational complexity

, Volume 15, Issue 2, pp 94–114 | Cite as

ON THE HARDNESS OF APPROXIMATING MULTICUT AND SPARSEST-CUT

  • Shuchi Chawla
  • Robert Krauthgamer
  • Ravi Kumar
  • Yuval Rabani
  • D. Sivakumar
Open Access
Original Paper

Abstract.

We show that the Multicut, Sparsest-Cut, and Min-2CNF ≡ Deletion problems are NP-hard to approximate within every constant factor, assuming the Unique Games Conjecture of Khot (2002). A quantitatively stronger version of the conjecture implies an inapproximability factor of \(\Omega(\sqrt{\log \log n}).\)

Keywords.

Multicut sparsest-cut unique games conjecture Fourier analysis 

Subject classification.

68Q17 

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  • Shuchi Chawla
    • 1
  • Robert Krauthgamer
    • 2
  • Ravi Kumar
    • 2
    • 4
  • Yuval Rabani
    • 3
  • D. Sivakumar
    • 2
    • 5
  1. 1.Computer Science DepartmentCarnegie Mellon UniversityPittsburghU.S.A
  2. 2.IBM Almaden Research CenterSan JoseU.S.A
  3. 3.Computer Science DepartmentTechnion—Israel Institute of TechnologyHaifaIsrael
  4. 4.Yahoo! ResearchSunnyvaleU.S.A
  5. 5.Google, Inc.Mountain ViewU.S.A

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