Lifted Cover Inequalities for 0-1 Integer Programs: Complexity

Published Online:https://doi.org/10.1287/ijoc.11.1.117

References

  • Balas E. Facets of the knapsack polytope. Math. Programming (1975) 8:146–164CrossrefGoogle Scholar
  • Balas E., Zemel E., Cottle R. W., Kennington H. L., Korte B. Lifting and complementing yields all the facets of positive zero-one programming polytopes. Mathematical Programming (1984) (North-Holland, Amsterdam)13–24Google Scholar
  • Chung C. S., Hung M. S., Rom W. O. A hard Knapsack problem. Naval Res. Logist. Quart. (1988) 35:85–98CrossrefGoogle Scholar
  • Chvatal V. Hard Knapsack problems. Oper. Res. (1980) 28:1402–1411LinkGoogle Scholar
  • Crowder H., Johnson E., Padberg M. Solving large-scale zero-one linear programming problems. Oper. Res. (1983) 31:803–834LinkGoogle Scholar
  • Garey M. R., Johnson D. S.Computers and Intractability: A Guide to the Theory of NP-Completeness (1979) (W. H. Freeman and Company, San Francisco) Google Scholar
  • Gu Z., Nemhauser G. L., Savelsbergh M. W. P. Lifted cover inequalities for 0-1 integer programs: Computation. INFORMS J. Comput. (1998) 10:427–437LinkGoogle Scholar
  • Gu Z., Nemhauser G. L., Savelsbergh M. W. P. Lifted cover inequalities for 0-1 integer programs: Algorithms. (1999) . Technical report, Georgia Institute of Technology, in PreparationGoogle Scholar
  • Hartvigsen D., Zemel E. The complexity of lifted inequalities for the Knapsack problem. Discrete Appl. Math. (1992) 39:113–123CrossrefGoogle Scholar
  • Hoffman K., Padberg M. Improving LP-representations of zero-one linear programs for branch-and-cut. ORSA J. Comput. (1991) 3:121–134LinkGoogle Scholar
  • Jereslow R. G. Trivial integer programs unsolved by branch and bound. Math. Programming (1974) 6:105–109CrossrefGoogle Scholar
  • Klabjan D., Nemhauser G. L., Tovey C. The complexity of cover inequality separation. Oper. Res. Lett. (1998) 23:35–40CrossrefGoogle Scholar
  • Laurent M., Sassano A. A characterization of Knapsacks with the max-flow-min-cut property. Oper. Res. Lett. (1992) 11:105–110CrossrefGoogle Scholar
  • Martello S., Toth P.Knapsack Problems: Algorithms and Computer Implementations (1990) (John Wiley and Sons, New York) Google Scholar
  • Nemhauser G. L., Vance P. H. Lifted cover facets of the 0-1 Knapsack polytope with GUB constraints. Oper. Res. Lett. (1994) 16:255–263CrossrefGoogle Scholar
  • Nemhauser G. L., Wolsey L. A.Integer and Combinatorial Optimization (1988) (John Wiley and Sons, New York) CrossrefGoogle Scholar
  • Padberg M. W. A note on zero-one programming. Oper. Res. (1975) 23:833–837LinkGoogle Scholar
  • Padberg M. W. (1 k)-configurations and facets for packing problems. Math. Programming (1980) 18:94–99CrossrefGoogle Scholar
  • Weismantel R. On the 0/1 Knapsack polytope. (1994) . Technical report SC 91-1, Konrad-Zuse-Zentrum fur Informationstechnik Berlin, Berlin, GermanyGoogle Scholar
  • Wolsey L. A. Faces for a linear inequality in 0-1 variables. Math. Programming (1975) 8:165–178CrossrefGoogle Scholar
  • Zemel E. Easily computable facets of the knapsack polytope. Math. Oper. Res. (1989) 14:760–765LinkGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.