On Disjunctive Cuts for Combinatorial Optimization

Journal of Combinatorial Optimization

Volumn 5, Issue 3, 2001, Pages 299-315

  Letchford, Adam N ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Asymmetric travelling salesman problem; Cutting planes; Integer programming; Max cut problem; Set covering problem

Indexed keywords

EID: 0042328182     PISSN: 13826905     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011493126498     Document Type: Article

References (42)

1. E. Balas, "Disjunctive programming," Annals of Discr. Math., vol. 5, pp. 3-51, 1979.
2. E. Balas, "Disjunctive programming: Properties of the convex hull of feasible points," Discr. Appl. Math., vol. 89, pp. 3-44, 1998.
3. E. Balas, S. Ceria, and G. Cornuéjols, "A lift-and-project cutting plane algorithm for mixed 0-1 programs," Math. Program., vol. 58, pp. 295-324, 1993.
4. E. Balas, S. Ceria, and G. Cornuéjols, "Mixed 0-1 programming by lift-and-project in a branch-and-cut framework," Mgt. Sci., vol. 42, pp. 1229-1246, 1996a.
5. E. Balas, S. Ceria, G. Cornuéjols, and N. Natraj, "Gomory cuts revisited," Oper. Res. Lett., vol. 19, pp. 1-9, 1996b.
6. E. Balas, S. Ceria, G. Cornuéjols, and G. Pataki, "Polyhedral methods for the maximum clique problem," Technical Report, Carnegie Mellon University, Pittsburgh, USA (1994).
7. E. Balas and R.G. Jeroslow, "Strengthening cuts for mixed integer programs," Eur. J. Opl Res., vol. 4, pp. 224-234, 1980.
8. E. Balas and S.M. Ng, "On the set covering polytope I: All the facets with coefficients in {0,1,2}," Math. Program., vol. 43, pp. 57-69, 1989.
9. F. Barahona and A.R. Mahjoub, "On the cut polytope," Math. Program., vol. 36, pp. 157-173, 1986.
10. R. Borndörfer and R. Weismantel, "Set packing relaxations of integer programs," Math. Program., vol. 88, pp. 425-450, 2000.
11. R. Borndörfer and R. Weismantel, "Discrete relaxations of combinatorial programs," Preprint SC 97-54, Zentrum für Informationstechnik, Berlin, 1997.
12. A. Caprara and M. Fischetti, "{0, 1/2}-Chvátal-Gomory cuts," Math. Program., vol. 74, pp. 221-235, 1996.
13. A. Caprara and M. Fischetti, "Branch-and-cut algorithms," in Annotated Bibliographies in Combinatorial Optimization, M. Dell'Amico, F. Maffioli, and S. Martello (Eds.), Wiley: New York, 1997.
14. S. Ceria, P. Nobili, and A. Sassano, "Set covering problem," in Annotated Bibliographies in Combinatorial Optimization, M. Dell'Amico, F. Maffioli, and S. Martello (Eds.), Wiley: New York, 1997.
15. S. Chopra and M.R. Rao, "The partition problem," Math. Program., vol. 59, pp. 87-115, 1993.
16. V. Chvátal, "Edmonds polytopes and a hierarchy of combinatorial problems," Discr. Math., vol. 4, pp. 305-337, 1973.
17. W. Cook, R. Kannan, and A.J. Schrijver, "Chvátal closures for mixed integer programming problems," Math. Program., vol. 47, pp. 155-174, 1990.
18. M. Deza, M. Grötschel, and M. Laurent, "Clique-web facets for multicut polytopes," Math. Oper. Res., vol. 17, pp. 981-1000, 1992.
19. J. Edmonds, "Maximum matching and a polyhedron with 0, 1-vertices," J. Res. Nat. Bur. Standards B, vol. 69, pp. 125-130, 1965.
20. R. Euler, M. Jünger, and G. Reinelt, "Generalizations of cliques, odd cycles and anticycles and their relation to independence system polyhedra," Math. Oper. Res., vol. 12, pp. 451-462, 1987.
21. M. Fischetti, "Facets of the asymmetric travelling salesman polytope," Math. Oper. Res., vol. 16, pp. 42-56, 1991.
22. M. Fischetti and P. Toth, "A polyhedral approach to the asymmetric travelling salesman problem," Management Science, vol. 43, pp. 1520-1536, 1997.
23. A.M.H. Gerards, "Testing the odd bicycle wheel inequalities for the bipartite subgraph polytope," Math. Oper. Res., vol. 10, pp. 359-360, 1985.
24. R.E. Gomory, "An algorithm for integer solutions to linear programs," in Recent Advances in Mathematical Programming, R.L. Graves and P. Wolfe (Eds.), McGraw-Hill: New York, 1963.
25. M. Grötschel, M. Jünger, and G. Reinelt, "On the acyclic subdigraph polytope," Math. Program., vol. 33, pp. 28-42, 1985a.
26. M. Grötschel, M. Jünger, and G. Reinelt, "Facets of the linear ordering polytope," Math. Program., vol. 33, pp. 43-60, 1985b.
27. M. Grötschel, L. Lovász, and A.J. Schrijver, Geometric Algorithms and Combinatorial Optimization, Wiley: New York, 1988.
28. M. Grötschel and M.W. Padberg, "Polyhedral theory," in The Traveling Salesman Problem, E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy-Kan, and D. Shmoys (Eds.), Wiley: Chichester, 1985.
29. M. Grötschel and Y. Wakabayashi, "Facets of the clique partitioning polytope," Math. Program., vol. 47, pp. 367-383, 1990.
30. K.L. Hoffman and M.W. Padberg, "Solving air-crew scheduling problems by branch-and-cut," Mgt. Sci., vol. 39, pp. 657-682, 1993.
31. L. Lovász and A.J. Schrijver, "Cones of matrices and set-functions and 0-1 optimization," SIAM J. Opn., vol. 1, pp. 166-190, 1991.
32. R. Müller and A. Schulz, "Transitive packing," in Integer Programming and Combinatorial Optimization, Lecture Notes in Computer Science 1084, W.H. Cunningham, S.T. McCormick, and M. Queyranne (Eds.), Springer: Berlin, 1996.
33. G.L. Nemhauser and L.A. Wolsey, Integer and Combinatorial Optimization, Wiley: New York, 1988.
34. G.L. Nemhauser and L.A. Wolsey, "A recursive procedure to generate all cuts for 0-1 mixed integer programs," Math. Program., vol. 46, pp. 379-390, 1990.
35. M.W. Padberg and M. Grötschel, "Polyhedral computations," in The Traveling Salesman Problem, E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy-Kan, and D. Shmoys (Eds.), Wiley: Chichester, 1985.
36. M.W. Padberg and M.R. Rao, "Odd minimum cut-sets and b-matchings," Math. Oper. Res., vol. 7, pp. 67-80, 1982.
37. M.W. Padberg and G. Rinaldi, "A branch-and-cut algorithm for the resolution of large-scale symmetric travelling salesman problems," SIAM Rev., vol. 33, pp. 60-100, 1991.
38. S. Poljak and D. Turzik, "Max-cut in circulant graphs," Discr. Math., vol. 108, pp. 379-392, 1992.
39. A. Sassano, "On the facial structure of the set covering polytope," Math. Program., vol. 44, pp. 181-202, 1989.
40. H.D. Sherali and W.P. Adams, "A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems," SIAM J. Discr. Math., vol. 3, pp. 411-430, 1990.
41. H.D. Sherali and Y. Lee, "Tighter representations for set partitioning problems," Discr. Appl. Math., vol. 68, pp. 153-167, 1996.
42. M. Yannakakis, "Expressing combinatorial optimization problems by linear programs," J. Compt. Syst. Sci., vol. 43, pp. 441-466, 1991.