Extending SDP integrality gaps to Sherali-Adams with applications to Quadratic Programming and MaxCutGain

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6080 LNCS, Issue , 2010, Pages 299-312

  Benabbas, Siavosh ^a   Magen, Avner ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRALITY GAPS; QUADRATIC PROGRAMMING PROBLEMS; SEMIDEFINITE RELAXATION;

COMBINATORIAL OPTIMIZATION; DYNAMIC PROGRAMMING; QUADRATIC PROGRAMMING;

INTEGER PROGRAMMING;

EID: 77954415978     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-13036-6_23     Document Type: Conference Paper

References (17)

1. Alon, N., Makarychev, K., Makarychev, Y., Naor, A.: Quadratic forms on graphs. Invent. Math. 163(3), 499-522 (2006)
2. Arora, S., Berger, E., Kindler, G., Safra, M., Hazan, E.: On non-approximability for quadratic programs. In: FOCS '05: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, pp. 206-215. IEEE Computer Society, Washington (2005)
3. Charikar, M., Makarychev, K., Makarychev, Y.: Integrality gaps for sherali-adams relaxations. In: STOC '09: Proceedings of the 41st annual ACM symposium on Theory of computing, pp. 283-292. ACM, New York (2009)
4. Charikar, M., Wirth, A.: Maximizing quadratic programs: Extending grothendieck's inequality. In: FOCS '04: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 54-60. IEEE Computer Society, Washington (2004)
5. Georgiou, K., Magen, A., Tulsiani, M.: Optimal sherali-adams gaps from pairwise independence. In: APPROX-RANDOM, pp. 125-139 (2009)
6. Grothendieck, A.: Résumeé de la theéorie meétrique des produits tensoriels topologiques. Bol. Soc. Mat. São Paulo 8, 1-79 (1953)
7. Khot, S., O'Donnell, R.: Sdp gaps and ugc-hardness for maxcutgain. In: FOCS '06: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, pp. 217-226. IEEE Computer Society, Washington (2006)
8. Lasserre, J.B.: An explicit exact sdp relaxation for nonlinear 0-1 programs. In: Aardal, K., Gerards, B. (eds.) IPCO 2001. LNCS, vol. 2081, pp. 293-303. Springer, Heidelberg (2001)
9. Lovaész, L., Schrijver, A.: Cones of matrices and set-functions and 0-1 optimization. SIAM Journal on Optimization 1(2), 166-190 (1991)
10. Mathieu, C., Sinclair, A.: Sherali-adams relaxations of the matching polytope. In: STOC '09: Proceedings of the 41st annual ACM symposium on Theory of computing, pp. 293-302. ACM, New York (2009)
11. Matousek, J.: Lectures on Discrete Geometry. Springer, New York (2002)
12. Raghavendra, P., Steurer, D.: How to round any csp. In: FOCS '09: Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science (to appear 2009)
13. Raghavendra, P., Steurer, D.: Integrality gaps for strong sdp relaxations of unique games. In: FOCS '09: Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science (to appear 2009)
14. Schoenebeck, G.: Linear level lasserre lower bounds for certain k-csps. In: FOCS '08: Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science, pp. 593-602. IEEE Computer Society, Washington (2008)
15. Sherali, H.D., Adams, W.P.: A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM Journal on Discrete Mathematics 3(3), 411-430 (1990)
16. Tulsiani, M.: Csp gaps and reductions in the lasserre hierarchy. In: STOC '09: Proceedings of the 41st annual ACM symposium on Theory of computing, pp. 303-312. ACM, New York (2009)
17. de la Vega,W.F., Kenyon-Mathieu, C.: Linear programming relaxations of maxcut. In: SODA '07: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 53-61. Society for Industrial and Applied Mathematics, Philadelphia (2007)