The UGC hardness threshold of the l p Grothendieck problem

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2008, Pages 64-73

  Kindler, Guy ^a   Naor, Assaf ^b   Schechtman, Gideon ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGEN VALUES; N MATRIX; NP-HARD; POLYNOMIAL-TIME; POLYNOMIAL-TIME ALGORITHMS; WALL POTENTIAL;

ALGORITHMS; CLUSTERING ALGORITHMS; GRAPH THEORY; HARDNESS; NUMBER THEORY; POLYNOMIAL APPROXIMATION;

APPROXIMATION ALGORITHMS;

EID: 58449126386     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (33)

1. D. Achlioptas, A. Naor, and Y. Peres. Rigorous location of phase transitions in hard optimization problems. Nature, 435:759-764, 2005.
2. A. Alon and E. Berger. The Grothendieck constant of random and pseudo-random graphs. To appear in Discrete Optimization.
3. N. Alon, K. Makarychev, Y. Makarychev, and A. Naor. Quadratic forms on graphs. Invent. Math., 163(3):499-522, 2006.
4. N. Alon and A. Naor. Approximating the cut-norm via Grothendieck's inequality. SIAM J. Comput., 35(4):787-803 (electronic), 2006.
5. S. Arora, E. Berger, G. Kindler, E. Hazan, and S. Safra. On non-approximability for quadratic programs. In 46th Annual Symposium on Foundations of Computer Science, pages 206-215. IEEE Computer Society, 2005.
6. E. Artin. The gamma function. Translated by Michael Butler. Athena Series: Selected Topics in Mathematics. Holt, Rinehart and Winston, New York, 1964.
7. C. P. Bachas. Computer-intractability of the frustration model of a spin glass. J. Phys. A: Math. Gen., 17:709-712, 1984.
8. N. Bansal, S. Bravyi, and B. M. Terhal. A classical approximation scheme for the ground-state energy of lsing spin Hamiltonians on planar graphs. Preprint, 2007.
9. F. Barahona. On the computational complexity of lsing spin glass models. J. Phys. A: Math. Gen., 15:3241-3253, 1981.
10. M. Bellare and P. Rogaway. The complexity of approximating a nonlinear program. Math. Programming, 69(3, Ser. A):429-441, 1995.
11. G. Ben Arous, A. Dembo, and A. Guionnet. Aging of spherical spin glasses. Probab. Theory Related Fields, 120(1):1-67, 2001.
12. L. Bieche, R. Maynard, R. Rammal, and J. P. Uhry. On the ground states of the frustration model of a spin glass by a matching method of graph theory. J. Phys. A: Math. Gen., 13:2553-2576, 1980.
13. A. Brieden. Geometric optimization problems likely not contained in A;ℙX. Discrete Comput. Geom., 28(2):201-209, 2002.
14. M. Charikar, K. Makarychev, and Y. Makarychev. Near-optimal algorithms for unique games (extended abstract). In STOC'06: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, pages 205-214, New York, 2006. ACM.
15. M. Charikar and A. Wirth. Maximizing quadratic programs: extending Grothendieck's inequality. In 45th Annual Symposium on Foundations of Computer Science, pages 54-60. IEEE Computer Society, 2004.
16. E. de Klerk, M. Laurent, and P. A. Parrilo. A PTAS for the minimization of polynomials of fixed degree over the simplex. Theoret. Comput. Sci., 361(2-3):210-225, 2006.
17. U. Feige and L. Lovasz. Two-prover one-round proof systems, their power and their problems. In STOC'92: Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 733-744, New York, 1992. ACM.
18. M. Grotschel, L. Lovász, and A. Schrijver. Geometric algorithms and combinatorial optimization, volume 2 of Algorithms and Combinatorics. Springer-Verlag, Berlin, second edition, 1993.
19. P. Hall. Rates of convergence in the central limit theorem, volume 62 of Research Notes in Mathematics. Pitman (Advanced Publishing Program), Boston, Mass., 1982.
20. E. Halperin and E. Hazan. HAPLOFREQ-estimating haplotype frequencies efficiently. J. Comput. Biol., 13(2):481-500 (electronic), 2006.
21. W. B. Johnson and J. Lindenstrauss. Basic concepts in the geometry of Banach spaces. In Handbook of the geometry of Banach spaces, Vol. I, pages 1-84. North-Holland, Amsterdam, 2001.
22. S. Khot. On the power of unique 2-prover 1-round games. In Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, pages 767-775 (electronic), New York, 2002. ACM.
23. S. Khot and R. O'Donnell. SDP gaps and UGC-hardness for MAXCUTGAIN. In 47th Annual Symposium on Foundations of Computer Science, pages 217-226. IEEE Computer Society, 2006.
24. J. Machta. The computational complexity of pattern formation. J. Stat. Phys., 70:949-966, 1993.
25. A. Megretski. Relaxation of quadratic programs in operator theory and system analysis. Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000), (3):365-392, 2001.
26. A. Megretski. Relaxations of quadratic programs in operator theory and system analysis. In Systems, approximation, singular integral operators, and related topics (Bordeaux, 2000), volume 129 of Oper. Theory Adv. Appl., pages 365-392. Birkhäuser, Basel, 2001.
27. A. Nemirovski, C. Roos, and T. Terlaky. On maximization of quadratic form over intersection of ellipsoids with common center. Math. Program., 86(3, Ser. A):463-473, 1999.
28. 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.
29. Y. Nesterov. Global quadratic optimization via conic relaxation. Working paper CORE, 1998.
30. H. Sompolinsky and A. Zippelius. Dynamic theory of the spin-glass phase. Phys. Rev. Lett., 47(5):359-362, 1981.
31. T.S. Motzkin and E. Straus. Maxima for graphs and a new proof of a theorem of turan. Canadian Journal of Mathematics, 17:533-540, 1965.
32. P. van Beek. An application of Fourier methods to the problem of sharpening the Berry-Esseen inequality. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 23:187-196, 1972.
33. S. Wolfram. Undecidability and intractability in theoretical physics. Phys. Rev. Lett., 54:735-738, 1985.