Lifted cover inequalities for 0-1 integer programs: Complexity

INFORMS Journal on Computing

Volumn 11, Issue 1, 1999, Pages 117-123

  Gu, Zonghao ^a   Nemhauser, George L ^a   Savelsbergh, Martin W P ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

Complexity of separation; Cutting plane; Separation algorithms

Indexed keywords

EID: 0242463701     PISSN: 10919856     EISSN: None     Source Type: Journal    
DOI: 10.1287/ijoc.11.1.117     Document Type: Article

References (21)

1. E. BALAS, 1975. Facets of the Knapsack Polytope, Mathematical Programming 8, 146-164.
2. E. BALAS and E. ZEMEL, 1984. Lifting and Complementing Yields All the Facets of Positive Zero-One Programming Polytopes, in Mathematical Programming, R.W. Cottle, H.L. Kennington, and B. Korte (eds.), North-Holland, Amsterdam, 13-24.
3. C.S. CHUNG, M.S. HUNG, and W.O. ROM, 1988. A Hard Knapsack Problem, Naval Research Logistics Quarterly 35, 85-98.
4. V. CHVATAL, 1980. Hard Knapsack Problems, Operations Research 28, 1402-1411.
5. H. CROWDER, E. JOHNSON, and M. PADBERG, 1983. Solving Large-Scale Zero-One Linear Programming Problems, Operations Research 31, 803-834.
6. M.R. GAREY and D.S. JOHNSON, 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman and Company, San Francisco.
7. Z. GU, G.L. NEMHAUSER, and M.W.P. SAVELSBERGH, 1998. Lifted Cover Inequalities for 0-1 Integer Programs: Computation, INFORMS Journal on Computing 10, 427-437.
8. Z. GU, G.L. NEMHAUSER, and M.W.P. SAVELSBERGH, 1999. Lifted Cover Inequalities for 0-1 Integer Programs: Algorithms, Technical Report, Georgia Institute of Technology, in preparation.
9. D. HARTVIGSEN and E. ZEMEL, 1992. The Complexity of Lifted Inequalities for the Knapsack Problem, Discrete Applied Mathematics 39, 113-123.
10. K. HOFFMAN and M. PADBERG, 1991. Improving LP-Representations of Zero-One Linear Programs for Branch-and-Cut, ORSA Journal of Computing 3, 121-134.
11. R.G. JERESLOW, 1974. Trivial Integer Programs Unsolved by Branch and Bound, Mathematical Programming 6, 105-109.
12. D. KLABJAN, G.L. NEMHAUSER, and C. TOVEY, 1998. The Complexity of Cover Inequality Separation, Operations Research Letters 23, 35-40.
13. M. LAURENT and A. SASSANO, 1992. A Characterization of Knapsacks with the Max-Flow-Min-Cut Property, Operations Research Letters 11, 105-110.
14. S. MARTELLO and P. TOTH, 1990. Knapsack Problems: Algorithms and Computer Implementations, John Wiley and Sons, New York.
15. G.L. NEMHAUSER and P.H. VANCE, 1994. Lifted Cover Facets of the 0-1 Knapsack Polytope with GUB Constraints, Operations Research Letters 16, 255-263.
16. G.L. NEMHAUSER and L.A. WOLSEY, 1988. Integer and Combinatorial Optimization, John Wiley and Sons, New York.
17. M.W. PADBERG, 1975. A Note on Zero-One Programming, Operations Research 23, 833-837.
18. M.W. PADBERG, 1980. (1, k)-Configurations and Facets for Packing Problems, Mathematical Programming 18, 94-99.
19. R. WEISMANTEL, 1994. On the 0/1 Knapsack Polytope, Technical Report SC 91-1, Konrad-Zuse-Zentrum fur Informationstechnik Berlin, Berlin, Germany.
20. L.A. WOLSEY, 1975. Faces for a Linear Inequality in 0-1 Variables, Mathematical Programming 8, 165-178.
21. E. ZEMEL, 1989. Easily Computable Facets of the Knapsack Polytope, Mathematics of Operations Research 14, 760-765.