SDP gaps and UGC hardness for multiway cut, O-extension, and metric labeling

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2008, Pages 11-20

  Manokaran, Rajsekar ^a   Naor, Joseph ^b   Raghavendra, Prasad ^c   Schwartz, Roy ^b  

^a Princeton University   (United States)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c University of Washington   (United States)

Author keywords

Integrality gaps; Linear and semidefinite programming; Metric labelling; Multiway cut; Unique games conjecture

Indexed keywords

INTEGRALITY GAPS; LINEAR AND SEMIDEFINITE PROGRAMMING; METRIC LABELLING; MULTIWAY CUT; UNIQUE GAMES CONJECTURE;

GAME THEORY; HARDNESS; LINEAR PROGRAMMING; LINEARIZATION; POLYNOMIAL APPROXIMATION; PROGRAMMING THEORY;

LABELING;

EID: 57049129456     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (26)

1. Aaron Archer, Jittat Fakcharoenphol, Chris Harrelson, Robert Krauthgamer, Knnal Talwar, and Éva, Tardos. Approximate classification via earthmover metrics. In SODA '0Jh: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1079-1087, 2004.
2. Per Austrin. Balanced max 2-sat might not be the hardest. In STOC '07: Proceedings of the 39th Annual ACM Symposium on Theory of Computing, pages 189-197, 2007.
3. Per Austrin. Towards sharp inapproximability for any 2-csp. In FOCS '07: Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, pages 307-317, 2007.
4. Yair Bartal. On approximating arbitrary metrices by tree metrics. In STOC '98: Proceedings of the 30th Annual ACM Symposium on Theory of Computing, pages 161-168, 1998.
5. Gruia Calinescu, Howard Karloff, and Yuval Rabani. Approximation algorithms for the O-extension problem. In SODA '01: Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 8-16, 2001.
6. Chandra Chekuri, Sanjeev Khanna, Joseph (Seffi) Naor, and Leonid Zosin. Approximation algorithms for the metric labeling problem via, a, new linear programming formulation. SIAM J. Disc. Math., 18:608-625, 2005.
7. Julia Chuzhoy and Joseph (SefB) Naor. The hardness of metric labeling. SIAM J. Comput., 36(5): 1376-1386, 2006.
8. Gruia Cǎlinescu, Howard Karloff, and Yuval Rabani. An improved approximation algorithm for multiway cut. In STOC '98: Proceedings of the 30th Annual ACM Symposium on Theory of Computing, pages 48-52, 1998.
9. Elias Dahlhaus, David Johnson, Christos Papadimitriou, Paul Seymour, and Mihalis Yannakakis. The complexity of multiway cuts (extended abstract). In STOC '92: Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 241-251, 1992.
10. Jittat Fakcharoenphol, Chris Harrelson, Satish Rao, and Kunal Talwar. An improved approximation algorithm for the O-extension problem. In SODA '03: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 257-265, 2003.
11. Jittat Fakcharoenphol, Satish Rao, and Kunal Talwar. Approximating metrics by tree metrics. SIC ACT News, 35(2):60-70, 2004.
12. Anupam Gupta and Éva, Tardos. A constant factor approximation algorithm for a class of classification problems. In STOC '00: Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, pages 652-658, 2000.
13. David R. Karger, Philip Klein, Cliff Stein, Mikkel Thorup, and Neal E. Young. Rounding algorithms for a geometric embedding of minimum multiway cut. In STOC '99: Proceedings of the 31st Annual ACM Symposium on Theory of Computing, pages 668-678, 1999.
14. Howard Karloff, Subhash Khot, Aranyak Mehta, and Yuval Rabani. On earthrnover distance, metric labeling, and O-extension. In STOC '06: Proceedings of the 38th Annual A CM Symposium on Theory of Computing, pages 547-556, 2006.
15. Alexander Karzanov, Minimum O-extension of graph metrics. Europ. J. Combinat., 19:71-101, 1998.
16. Alexander Karzanov. A combinatorial algorithm for the minimum (2, r)-metric problem and some generalizations. Combinatorica, 18:549-569, 1999.
17. Subhash Khot. On the power of unique 2-prover 1-round games. In STOC '02: Proceedings of the 34th Annual ACM Symposium on Theory of Computing, pages 767-775, 2002.
18. Subhash Khot, Guy Kindler, Elchanan Mossel, and Ryan O'Donnell. Optimal inapproximability results for max-cut and other 2-variable csps? In FOCS '04: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pages 146-154, 2004.
19. Subhash Khot and Ryan O'Donnell. SDP gaps and UGC-hardness for maxcutgain. In FOCS '06: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, pages 217-226, 2006.
20. Subhash Khot and Oded R.egev. Vertex cover might be hard to approximate to within 2-ε. J. Comput. Syst. Sci., 74(3):335-349, 2008.
21. 1. In FOCS '05: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, pages 53-62, 2005.
22. Jon Kleinberg and Éva Tardos. Approximation algorithms for classification problems with pairwise relationships: metric labeling and markov random fields. J. ACM, 49(5):616-639, 2002.
23. Robert Krauthgamer, James R. Lee, Manor Mendel, and Assaf Naor. Measured descent: A new embedding method for finite metrics. In FOCS '04: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pages 434-443, 2004.
24. James R. Lee and Assaf Naor. Extending lipschitz functions via random metric partitions. Inventiones Mathematicae, 160(l):59-95, 2005.
25. Elchanan Mossel, Ryan O'Donnell, and Krzysztof Oleszkiewicz. Noise stability of functions with low influences: Invariance and optimality. In FOCS '05: Proceedings of the 496th Annual IEEE Symposium on Foundations of Computer Science, pages 21-30, 2005.
26. Prasad Raghavendra,. Optimal algorithms and inapproximability results for every csp? In STOC '08: Proceedings of the 40th A CM Symposium on Theory of Computing, 2008.