A Unified Framework for Obtaining Improved Approximation Algorithms for Maximum Graph Bisection Problems

Random Structures and Algorithms

Volumn 20, Issue 3, 2002, Pages 382-402

  Halperin, Eran ^a   Zwick, Uri ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036099181     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/rsa.10035     Document Type: Conference Paper

References (23)

1. A. Ageev, R. Hassin, and M. Sviridenko, An 0.5-approximation algorithm for MAX DICUT with given sizes of parts, manuscript, 2000.
2. F. Barahona and A. R. Mahjoub, On the cut polytope, Math Program 36 (1986), 157-173.
3. U. Feige and M. X. Goemans, Approximating the value of two prover proof systems, with applications to MAX-2SAT and MAX-DICUT, Proc 3rd Israel Symp Theory and Computing Systems, Tel Aviv, Israel, 1995, pp. 182-189.
4. U. Feige and M. Langberg, Approximation algorithms for maximization problems arising in graph partitioning, manuscript, 1999.
5. 2 rounding technique for semidefinite programs, Proc 28th Int Colloq Automata, Languages and Programming, Crete, Greece, 2001, pp. 213-224.
6. U. Feige and G. Schechtman, On the integrality ratio of semidefinite relaxations of MAX CUT, Proc 33th Annu ACM Symp Theory of Computing, Crete, Greece, 2001, to appear.
7. U. Feige, M. Karpinski, and M. Langberg, Improved approximation of Max-Cut on graphs of bounded degree, Technical Report, Electronic Colloquium on Computational Complexity, (E-CCC), University of Trier, Report No. TR00-043, 2000.
8. U. Feige, M. Karpinski, and M. Langberg, A note on approximating MAX-BISECTION on regular graphs, Technical Report, Electronic Colloquium on Computational Complexity, (E-CCC), University of Trier, Report No. TR00-043, 2000.
9. A. M. Frieze and M. Jerrum, Improved approximation algorithms for MAX k-CUT and MAX BISECTION, Algorithmica 18 (1997), 67-81.
10. M. X. Goemans and D. P. Williamson, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, J Appl Comput Math 42 (1995), 1115-1145.
11. M. Grötschel, L. Lovász, and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica 1 (1981), 169-197.
12. Q. Han, Y. Ye, and J. Zhang, An improved rounding method and semidefinite programming relaxation for graph partition, manuscript, 2000.
13. Q. Han, Y. Ye, H. Zhang, and J. Zhang, On approximation of Max-Vertex-Cover, manuscript, 2000.
14. H. Karloff and U. Zwick, A 7/8-approximation algorithm for MAX 3SAT? Proc 38th Annu IEEE Symp Foundations of Computer Science, Miami Beach, Florida, 1997, pp. 406-415.
15. S. Mahajan and H. Ramesh, Derandomizing approximation algorithms based on semidefinite programming, SIAM J Comput 28 (1999), 1641-1663.
16. Y. E. Nesterov, Semidefinite relaxation and nonconvex quadratic optimization, Optim Methods Software 9 (1998), 141-160.
17. P. Turán, On an extremal problem in graph theory, Mat Fiz Lapok 48 (1941), 436-452.
18. H. Wolkowicz, R. Saigal, and L. Vandenberghe (Eds.), Handbook of semidefinite programming, Kluwer, Boston, 2000.
19. Y. Ye, A 0.699-approximation algorithm for Max-Bisection, manuscript, 1999.
20. Y. Ye and J. Zhang, Approximation of dense-n/2-subgraph and the complement of min-bisection, manuscript, 1999.
21. U. Zwick, Outward rotations: A tool for rounding solutions of semidefinite programming relaxations, with applications to max cut and other problems, Proc 31th Annu ACM Symp Theory of Computing, Atlanta, Georgia, 1999, pp. 679-687.
22. U. Zwick, Analyzing the MAX 2-SAT and MAX DI-CUT approximation algorithms of Feige and Goemans, 2000, submitted for publication.
23. U. Zwick, Computer assisted proof of optimal approximability results, Proc 13th Annu ACM-SIAM Symp Discrete Algorithms, San Francisco, California, 2002, pp. 496-505.