On semidefinite programming relaxations of (2 + p)-SAT

Annals of Mathematics and Artificial Intelligence

Volumn 37, Issue 3, 2003, Pages 285-305

  De Klerk, E ^a   Van Maaren, H ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Approximation algorithms; Randomized rounding; Satisfiability; Semidefinite programming

Indexed keywords

EID: 0037212943     PISSN: 10122443     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021208315170     Document Type: Article

References (23)

1. D. Achlioptas, L.M. Kirousis, E. Kranakis and D. Krizank, Rigorous results for random (2 + p)-SAT, Theoretical Computer Science 265(15) (2001) 109-129.
2. D.V. Alekseevskij, E.B. Vinberg and A.S. Solodovnikov, Geometry of spaces of constant curvature, in: Geometry II, ed. E.B. Vinberg, Encyclopedia of Mathematical Sciences, Vol. 29 (Springer, Berlin, 1993).
3. M.S. Bazarraa, H.D. Sherali and C.M. Shetty, Nonlinear Programming: Theory and Algorithms, 2nd edn. (Wiley, New York, 1993).
4. S.J. Benson, Y. Ye and X. Zhang, Solving large-scale sparse semidefinite programs for combinatorial optimization, SIAM Journal on Optimization 10 (2000) 443-461.
5. S.J. Benson and Y. Ye, DSDP3: Dual scaling algorithm for general positive semidefinite programming, Working paper, Computational Optimization Laboratory, Department of Management Science, University of Iowa, Iowa City (2001).
6. W. Cook, C.R. Coullard and G. Turan, On the complexity of cutting plane proofs, Discrete Applied Mathematics 18 (1987) 25-38.
7. C. Choi and Y. Ye, Solving sparse semidefinite programs using the dual scaling algorithm with an iterative solver, Working paper, Computational Optimization Laboratory, Department of Management Science, University of Iowa, Iowa City (2000).
8. E. de Klerk, C. Roos and T. Terlaky, Initialization in semidefinite programming via a self-dual, skew-symmetric embedding, OR Letters 20 (1997) 213-221.
9. E. de Klerk, C. Roos and T. Terlaky, Infeasible-start semidefinite programming algorithms via self-dual embeddings, in: Topics in Semidefinite and Interior-Point Methods, eds. P.M. Pardalos and H. Wolkowicz, Fields Institute Communications Series, Vol. 18 (American Mathematical Society, 1998) pp. 215-236.
10. E. de Klerk, H. van Maaren and J.P. Warners, Relaxations of the satisfiability problem using semidefinite programming, Journal of Automated Reasoning 24 (2000) 37-65.
11. M.X. Goemans and D.P. Williamson, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, Journal of the ACM 42(6) (1995) 1115-1145.
12. A. Haken, The intractability of resolution, Theoretical Computer Science 39 (1985) 297-308.
13. E. Halperin and U. Zwick, Approximation algorithms for MAX 4-SAT and rounding procedures for semidefinite programs, Journal of Algorithms 40 (2001) 184-211.
14. W.-Y. Hsiang, On infinitesimal symmetrization and volume formula for spherical or hyperbolic tetrahedrons, The Quarterly Journal of Mathematics. Oxford 39(2) (1988) pp. 463-468.
15. H. Karloff and U. Zwick, A 7/8-approximation algorithm for MAX 3SAT?, in: Proc. 38th FOCS (1997) 406-415.
16. L. Lovász, On the Shannon capacity of a graph, IEEE Transactions on Information Theory 25 (1979) 1-7.
17. S. Mahajan and H. Ramesh, Derandomizing semidefinite programming based approximation algorithms, in: Proc. of the 36th Annual IEEE Symposium on Foundations of Computer Science (1995) pp. 162-169.
18. R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman and L. Troyansky, Determining computational complexity from characteristic 'phase transitions', Nature 400 (1999) 133-137.
19. R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman and L. Troyansky, 2 + P-SAT: relation of typical-case complexity to the nature of the phase transition, Random Structure and Algorithms 15 (1999) 414-435.
20. J.F. Sturm, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optimization Methods and Software 11-12 (1999) 625-653.
21. H. Van Maaren, Elliptic approximations of propositional formulae, Discrete Applied Mathematics 96-97 (1999) 223-244.
22. J.P. Warners and H. Van Maaren, Recognition of tractable satisfiability problems through balanced polynomial representations, Discrete Applied Mathematics 99 (2000) 229-244.
23. U. Zwick, Outward rotations: a new tool for rounding solutions of semidefinite programming relaxations, with applications to MAX CUT and other problems, in: Proc. 31st STOC (1999) pp. 679-687.