Towards computing the Grothendieck constant

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2009, Pages 525-534

  Raghavendra, Prasad ^a   Steurer, David ^b  

^a University of Washington   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR PROGRAMMING; MATRIX ALGEBRA; NUMBER THEORY; QUADRATIC PROGRAMMING;

APPROXIMATION RATIOS; HARDNESS RESULT; INTEGRALITY GAPS; LINEAR PROGRAMS; OPTIMAL APPROXIMATION; QUADRATIC PROGRAMMING PROBLEMS; SDP RELAXATION; UNIQUE GAMES CONJECTURE;

APPROXIMATION ALGORITHMS;

EID: 70349138408     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973068.58     Document Type: Conference Paper

References (23)

1. N. Alon, K. Makarychev, Y. Makarychev, and A. Naor. Quadratic forms on graphs. In STOC, pages 486-493, 2005.
2. N. Alon and A. Naor. Approximating the cut-norm via Grothendieck's inequality. SIAM J. Comput, 35(4):787-803, 2006.
3. S. Arora, E. Berger, E. Hazan, G. Kindler, and M. Safra. On non-approximability for quadratic programs. In FOCS, pages 206-215, 2005.
4. A. Coja-Oghlan, C. Cooper, A. Frieze. An efficiently regular concept for sparse graphs and matrices. To appear in SODA, 2009.
5. B.W. Johnson and J. Lindenstrauss. Basic concepts in the geometry of Banach spaces. Handbook of the geometry of Banach spaces, North Holland, Amsterdam, 1:1-84, 2001.
6. M. Charikar and A. Wirth. Maximizing quadratic programs: Extending Grothendieck's inequality. In FOCS, pages 54-60, 2004. (Pubitemid 40575266)
7. A. Frieze and R. Kannan. Quick approximation to matrices and applications. Combinatorica, 19(2):175-220, 1999.
8. A. Grothendieck. Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat, 8:1-79, 1953.
9. S. Khot. On the power of unique 2-prover 1-round games. In STOC, pages 767-775, 2002. (Pubitemid 35009440)
10. 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.
11. S. Khot and R. O'Donnell. SDP gaps and UGC-hardness for MAXCUTGAIN. In FOCS, pages 217-226, 2006. (Pubitemid 351175511)
12. 1. In FOCS, pages 53-62, 2005. (Pubitemid 44375719)
13. p Grothendieck problem. In SODA, pages 64-73, 2008.
14. H. König. Spherical functions and the Grothendieck inequality. Unpublished manuscript, 2005. Available at http://shrimp.bayou.uni-linz.ac.at/ Vienna2005/pdf/koenig.pdf.
15. J. L. Krivine. Constantes de Grothendieck et fonctions de type positif sur les sphères. Adv. Math., 31:16-30, 1977-1978.
16. p spaces and their applications. Studia Math, 29:275-326, 1968.
17. N. Linial and A. Shraibman. Lower bounds in communication complexity based on factorization norms. In STOC, pages 699-708, 2007. (Pubitemid 47630789)
18. A. Megretski. Relaxation of quadratic programming in operator theory and systems analysis. Systems, approximation, singular integral operators and related topics, 2001.
19. E. Mossel. Gaussian bounds for noise correlation of functions. Submitted. Extended abstract appeared in FOCS, 2008.
20. E. Mossel, R. O'Donnell, and K. Oleszkiewicz. Noise stability of functions with low influences: invariance and optimality. To appear in Ann. Math., 2008.
21. A. Nemirovski, C. Roos, and T. Terlaky. On maximization of quadratic form over intersection of ellipsoids with common center. Mathematical Programming, 86(3):463-473, 1999.
22. P. Raghavendra. Optimal algorithms and inapproximability results for every CSP? In STOC, pages 245-254, 2008.
23. J. Reeds. A new lower bound on the real Grothendieck constant. Unpublished Manuscript, 1993. Available at http://www.dtc.umn.edu/~reedsj.