On the hardness of approximating multicut and sparsest-cut

Proceedings of the Annual IEEE Conference on Computational Complexity

Volumn , Issue , 2005, Pages 144-153

  Chawla, Shuchi ^a   Krauthgamer, Robert ^b   Kumar, Ravi ^b   Rabani, Yuval ^c   Sivakumar, D ^b  

^a Carnegie Mellon University   (United States)

^b IBM ALMADEN RESEARCH CENTER   (United States)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY CONSTANT FACTOR; INAPPROXIMABILITY FACTOR; UNIQUE GAMES CONJECTURE;

APPROXIMATION THEORY; PROBLEM SOLVING;

COMPUTATIONAL COMPLEXITY;

EID: 27644478310     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCC.2005.20     Document Type: Conference Paper

References (29)

1. A. Agarwal, M. Charikar, K. Makarychev, and Y. Makarychev. O(√log n) approximation algorithms for Min UnCut, Min 2CNF Deletion, and directed cut problems. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing, 2005.
2. S. Arora, J. R. Lee, and A. Naor. Euclidean distortion and the sparsest cut. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing, 2005.
3. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and the hardness of approximation problems. Journal of the ACM, 45(3):501-555, 1998.
4. S. Arora, S. Rao, and U. Vazirani. Expander flows, geometric embeddings, and graph partitionings. In Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pages 222-231, 2004.
5. S. Arora and S. Safra. Probabilistic checking of proofs: A new characterization of NP. Journal of the ACM, 45(1):70-122, 1998.
6. Y. Aumann and Y. Rabani. An O(log k) approximate mincut max-flow theorem and approximation algorithm. SIAM Journal on Computing, 27(1):291-301, 1998.
7. N. Bansal, A. Blum, and S. Chawla. Correlation Clustering. Machine Learning, Special Issue on Clustering, 56(1-3):89-113, 2004.
8. M. Bellare, O. Goldreich, and M. Sudan. Free bits, PCP's and non-approximability - towards tight results. SIAM Journal on Computing, 27(3):804-915, 1998.
9. M. Ben-Or and N. Linial. Collective coin flipping. In Randomness and Computation, pages 91-115, 1990.
10. M. Charikar, V. Guruswami, and A. Wirth. Clustering with qualitative information. In Proceedings of the 44th IEEE Symposium on Foundations of Computer Science, pages 524-533, 2003.
11. S. Chawla, A. Gupta, and H. Räcke. Improved approximations to sparsest cut. In Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 102-111, 2005.
12. E. Dahlhaus, D. S. Johnson, C. H. Papadimitriou, P. D. Seymour, and M. Yannakakis. The complexity of multiterminal cuts. SIAM Journal on Computing, 23(4):864-894, 1994.
13. E. Demaine and N. Immorlica. Correlation clustering with partial information. In Proceedings of the 6th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX), pages 1-13, 2003.
14. D. Emanuel and A. Fiat. Correlation clustering -minimizing disagreements on arbitrary weighted graphs. In Proceedings of 11th Annual European Symposium on Algorithms, pages 208-220, 2003.
15. U. Feige and D. Reichman. On systems of linear equations with two variables per equation. In Proceedings of the 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX), pages 117-127, 2004.
16. N. Garg, V. V. Vazirani, and M. Yannakakis. Approximate max-flow min-(multi)cut theorems and their applications. SIAM Journal on Computing, 25(2):235-251, 1996.
17. J. Håstad. Some optimal inapproximability results. Journal of the ACM, 48(4):798-859, 2001.
18. J. Kahn, G. Kalai, and N. Linial. The influence of variables on boolean functions. In Proceedings of the 29th IEEE Symposium on Foundations of Computer Science, pages 68-80, 1988.
19. S. Khot. On the power of unique 2-prover 1-round games. In Proceedings of the 34th Annual ACM Symposium on Theory of Computing, pages 767-775, 2002.
20. S. Khot, G. Kindler, E. Mossel, and R. O'Donnell. Optimal inapproximability results for MAX-CUT and other 2-variable CSPs. In Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, pages 146-154, 2004.
21. S. Khot and O. Regev. Vertex cover might be hard to approximate to within 2-ε. In Proceedings of the 18th Annual IEEE Conference on Computational Complexity, pages 379-386, 2003.
22. 1. Manuscript, 2004.
23. P. Klein, A. Agrawal, R. Ravi, and S. Rao. Approximation through multicommodity flow. In Proceedings of the 31st IEEE Symposium on Foundations of Computer Science, pages 726-737, 1990.
24. R. Kumar, D. Sivakumar, and E. Vee. Manuscript, 2005.
25. F. T. Leighton and S. Rao. An approximate max-flow mincut theorem for uniform multicommodity flow problems with applications to approximation algorithms. In Proceedings of the 29th IEEE Symposium on Foundations of Computer Science, pages 422-431, 1988.
26. N. Linial, E. London, and Y. Rabinovich. The geometry of graphs and some of its algorithmic applications. Combinatorica, 15(2):215-245, 1995.
27. E. Mossel, R. O'Donnell, and K. Oleszkiewicz. Noise stability of functions with low influences: Invariance and optimality. Manuscript, 2005.
28. R. Raz. A parallel repetition theorem. SIAM Journal on Computing, 27(3):763-803, 1998.
29. D. Stefankovic. Fourier Transforms in Computer Science. PhD thesis, University of Chicago, 2000.