On the hardness of approximating multicut and sparsest-cut

Shuchi Chawla*, Robert Krauthgamer, Ravi Kumar, Yuval Rabani, D. Sivakumar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

148 Scopus citations


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 Ω(√log log n).

Original languageAmerican English
Pages (from-to)94-114
Number of pages21
JournalComputational Complexity
Issue number2
StatePublished - Jun 2006
Externally publishedYes

Bibliographical note

Funding Information:
We thank the anonymous referees for useful comments, and in particular for suggesting a simplification of our original proof of Lemma 3.1. Part of this work was done while Shuchi Chawla was visiting IBM Almaden Research Center. Part of this work was done while Yuval Rabani was on sabbatical leave at Cornell University, while visiting IBM Almaden Research Center, and while visiting the Institute for Pure and Applied Mathematics at UCLA; his research at the Technion was supported in part by ISF grant number 52/03 and BSF grant number 02-00282. This work was done while Ravi Kumar and D. Sivakumar were at the IBM Almaden Research Center. A preliminary version of this paper appeared in Proceedings of 20th Annual IEEE Conference on Computational Complexity (CCC 2005).


  • Fourier analysis
  • Multicut
  • Sparsest-cut
  • Unique games conjecture


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