Unique games with entangled provers are easy

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2008, Pages 457-466

  Kempe, Julia ^a   Regevt, Oded ^a   Toner, Ben ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTERS; FIBER OPTIC CHEMICAL SENSORS;

PARALLEL REPETITIONS; ROUNDING TECHNIQUES; SEMIDEFINITE PROGRAMS; UNIQUE GAMES CONJECTURES;

GAME THEORY;

EID: 57949100465     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2008.9     Document Type: Conference Paper

References (36)

1. S. Arora, S. Khot, A. Kolla, D. Steurer, M. Tulsiani, and N. Vishnoi. Unique games on expanding constraint graphs are easy: extended abstract. In Proc. 40th ACM Symp. on Theory of Computing, pages 21-28, 2008.
2. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and the hardness of approximation problems. J. ACM, 45(3):501-555, 1998.
3. S. Arora and S. Safra. Probabilistic checking of proofs: a new characterization of NP. J. ACM, 45(1):70-122, 1998.
4. J. S. Bell. On the Einstein-Podolsky-Rosen paradox. Physics, 1:195-200, 1964.
5. S. Boyd and L. Vandenberghe. Convex optimization. Cambridge University Press, Cambridge, 2004.
6. H. Buhrman and S. Massar. Causality and Cirel'son bounds. quant-ph/0409066, 2004.
7. M. Charikar, K. Makarychev, and Y. Makarychev. Nearoptimal algorithms for unique games (extended abstract). In Proc. 38th ACM Symp. on Theory of Computing, pages 205-214, 2006.
8. S. Chawla, R. Krauthgamer, R. Kumar, Y. Rabani, and D. Sivakumar. On the hardness of approximating multicut and sparsest-cut. Comput. Complexity, 15(2):94-114, 2006.
9. E. Chlamtac, K. Makarychev, and Y. Makarychev. How to play unique games using embeddings. In Proc. 47th IEEE Symp. on Foundations of Computer Science, pages 687-696, 2006.
10. B. S. Cirel'son. Quantum generalizations of Bell's inequality. Lett. Math. Phys., 4:93-100, 1980.
11. J. F. Clauser, M. A. Home, A. Shimony, and R. A. Holt. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett., 23:880-884, 1969.
12. R. Cleve, P. Høyer, B. Toner, and J. Watrous. Consequences and limits of nonlocal strategies. In Proc. 19th IEEE Conference on Computational Complexity, pages 236-249, 2004.
13. R. Cleve, W. Slofstra, F. Unger, and S. Upadhyay. Perfect parallel repetition theorem for quantum XOR proof systems. In Proc. 22nd IEEE Conference on Computational Complexity, pages 109-114, 2007.
14. I. Dinur, E. Mossel, and O. Regev. Conditional hardness for approximate coloring. In Proc. 38th ACM Symp. on Theory of Computing, pages 344-353, 2006.
15. I. Dinur and S. Safra. On the hardness of approximating minimum vertex cover. Ann. of Math. (2), 162(1):439-485, 2005.
16. A. Einstein, P. Podolsky, and N. Rosen. Can quantummechanical description of physical reality be considered complete? Phys. Rev., 47:777-780, 1935.
17. U. Feige. A threshold of In n for approximating set cover. J. ACM, 45(4):634-652, 1998.
18. U. Feige and L. Lovász. Two-prover one-round proof systems: Their power and their problems. In Proc. 24th ACM Symp. on Theory of Computing, pages 733-741, 1992.
19. M. X. Goemans and D. P. Williamson. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. Assoc. Comput. Mach., 42(6):1115-1145, 1995.
20. A. Gupta and K. Talwar. Approximating unique games. In Proc. 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 99-106, 2006.
21. 1-ε. Acta Math., 182(1):105-142, 1999.
22. J. Håstad. Some optimal inapproximability results. J. ACM, 48(4):798-859, 2001.
23. T. Holenstein. Parallel repetition: simplifications and the no-signaling case. In Proc. 39th ACM Symp. on Theory of Computing, pages 411-419, 2007.
24. J. Kempe, H. Kobayashi, K. Matsumoto, B. Toner, and T. Vidick. Entangled games are hard to approximate. In Proc. 49th IEEE Symp. on Foundations of Computer Science, 2008.
25. J. Kempe, O. Regev, and B. Toner. The unique games conjecture with entangled provers is false. arXiv:0710.0655, 2007.
26. S. Khot. On the power of unique 2-prover 1-round games. In Proc. 34th ACM Symp. on Theory of Computing, pages 767-775, 2002.
27. S. Khot, G. Kindler, E. Mossel, and R. O'Donnell. Optimal inapproximability results for max-cut and other 2-variable CSPs? SIAM J. Comput, 37(1):319-357, 2007.
28. S. Khot and O. Regev. Vertex cover might be hard to approximate to within 2 - ε. In Proc. 18th IEEE Conference on Computational Complexity, pages 379-386, 2003.
29. S. Khot and N. K. Vishnoi. The unique games conjecture, integrality gap for cut problems and embeddability of negative type metrics into ¿j. In Proc. 46th IEEE Symp. on Foundations of Computer Science, pages 53-62, 2005.
30. L. Masanes. Extremal quantum correlations for N parties with two dichotomic observables per site, quant-ph/0512100, 2005.
31. R. Mittal and M. Szegedy. Product rules in semidefinite programming. In Proc. 16th Fund. Computation Theory (FCT), pages 435-445, 2007.
32. M. Navascues, S. Pironio, and A. Acín. Bounding the set of quantum correlations. Phys. Rev. Lett., 98(1):010401, 2007.
33. M. A. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, New York, 2000.
34. A. Rao. Parallel repetition in projection games and a concentration bound. In Proc. 40th ACM Symp. on Theory of Computing, pages 1-10, 2008.
35. R. Raz. A parallel repetition theorem. SIAM J. Comput., 27(3):763-803, 1998.
36. L. Trevisan. Approximation algorithms for unique games. In Proc. 46th IEEE Symp. on Foundations of Computer Science, pages 197-205, 2005.