Rank bounds and integrality gaps for cutting planes procedures

Annual Symposium on Foundations of Computer Science - Proceedings

Volumn , Issue , 2003, Pages 318-326

  Buresh Oppenheim, Joshua ^a   Galesi, Nicola ^b   Hoory, Shlomo ^a   Magen, Avner ^a   Pitassi, Toniann ^a  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGER PROGRAMMING; LINEAR PROGRAMMING; POLYNOMIALS; THEOREM PROVING;

CUTTING PLANES; INTEGRALITY GAPS; RANK BOUNDS; UNSATISFIABILITY;

COMPUTATIONAL COMPLEXITY;

EID: 85042391519     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (26)

1. Arora, Bollobas, and Lovasz. Proving integrality gaps without knowing the linear program. In FOCS: IEEE Symposium on Foundations of Computer Science (FOCS), 2002.
2. A. Atserias, M. L. Bonet, and J. Levy. On chvátal rank and cutting planes proofs. Manuscript, 2003.
3. E. Ben-Sasson and A. Wigderson. Short proofs are narrow - resolution made simple. In Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, pages 517-526, Atlanta, GA, May 1999.
4. A. Bockmayr, F. Eisenbrand, M. Hartmann, and A. Schulz. On the chvatal rank of polytopes in the 0/1 cube. Technical Report 616, Technical University of Berlin, Department of Mathematics, Saarbruecken, Dec. 1998.
5. M. Bonet and N. Galesi. A study of proof search algorithms for resolution and polynomial calculus. 1999.
6. V. Chvátal. Edmonds polytopes and a hierarchy of combinatorial problems. Discrete Mathematics, 4, 1973.
7. V. Chvátal, W. Cook, and M. Hartmann. On cutting-plane proofs in combinatorial optimization. Linear Algebra and its Applications, 114/115:455-499, 1989.
8. W. Cook, C. R. Coullard, and G. Turan. On the complexity of cutting plane proofs. Discrete Applied Mathematics, 18:25-38, 1987.
9. S. Dash. On the matrix cuts of Lovász and Schrijver and their use in Integer Programming. PhD thesis, Department of Computer Science, Rice University, Mar. 2001.
10. S. Dash. An exponential lower bound on the length of some classes of branch-and-cut proofs. In IPCO, 2002.
11. F. Eisenbrand and A. S. Schulz. Bounds on the Chvatal rank of polytopes in the 0/1-cube. Lecture Notes in Computer Science, 1610:137-??, 1999.
12. U. Feige and R. Krauthgamer. The probable value of lovász-schrijver relaxations for maximum independent set. SIAM Journal on Computing, 32(2):345-370, 2003.
13. M. Goemans and L. Tunçel. When does the positive semidefiniteness constraint help in lifting procedures. Mathematics of Operations Research, 26:796-815, 2001.
14. R. Gomory. Outline of an algorithm for integer solutions to linear programs. Bulletin of the American Mathematical Society, 64:275-278, 1958.
15. R. E. Gomory. Solving linear programming problems in integers. In R. Bellman and M. Hall, Jr., editors, Combinatorial Analysis, pages 211-215, Providence, RI, 1960. Symposia in Applied Mathematics X, American Mathematical Society.
16. D. Grigoriev, E. A. Hirsch, and D. V. Pasechnik. Complexity of semi-algebraic proofs. In Symposium on Theoretical Aspects of Computer Science, pages 419-430, 2002.
17. D. Grigoriev, E. A. Hirsch, and D. V. Pasechnik. Exponential lower bound for static semi-algebraic proofs. Lecture notes in computer science, 2380:257-268, 2002.
18. M. Grötschel, L. Lovász, and A. Schrijver. Geometric algorithms and combinatorial optimization, volume 2 of Algorithms and Combinatorics. Springer-Verlag, Berlin, second edition, 1993.
19. A. Haken. The intractability of resolution. Theoretical Computer Science, 39:297-305, 1985.
20. E. Hirsch and A. Kojevnikov. Several notes on the power of gomory-chvatal cuts. Technical Report TR03-012, ECCC, 2003.
21. R. Impagliazzo, T. Pitassi, and A. Urquhart. Upper and lower bounds on tree-like cutting planes proofs. In Proceedings from Logic in Computer Science, 1994.
22. L. G. Khachian. A polynomial time algorithm for linear programming. Doklady Akademii Nauk SSSR, n.s., 244(5):1093-1096, 1979. English translation in Soviet Math. Dokl. 20, 191-194.
23. B. Krishnamurthy. Short proofs for tricky formulas. Acta Informatica, 22:253-275, 1985.
24. L. Lovász and A. Schrijver. Cones of matrices and set-functions and 0-1 optimization. SIAM J. Optimization, 1(2):166-190, 1991.
25. P. Pudlák. Lower bounds for resolution and cutting plane proofs and monotone computations. Journal of Symbolic Logic, 62(3):981-998, Sept. 1997.
26. G. Stalmark. Short resolution proofs for a sequence of tricky formulas. Acta Informatica, 33:277-280, 1996.