Binary clutter inequalities for integer programs

Mathematical Programming

Volumn 98, Issue 1-3, 2003, Pages 201-221

  Letchford, Adam N ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Binary clutters; Cutting planes; Integer programming; Matroid theory; Traveling salesman problem

Indexed keywords

BINARY CLUTTER; CUTTING PLANES; INTEGER LINEAR PROGRAMS; MATROID THEORY; POLYNOMIALLY SOLVABLE; SEPARATION PROBLEMS; STRONGLY NP-HARD; VALID INEQUALITY;

CLUTTER (INFORMATION THEORY); COMBINATORIAL MATHEMATICS; MATRIX ALGEBRA; POLYNOMIAL APPROXIMATION; SEPARATION; TRAVELING SALESMAN PROBLEM;

INTEGER PROGRAMMING;

EID: 33847196534     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-003-0402-x     Document Type: Conference Paper

References (34)

1. Applegate, D., Bixby, R.E., Chvátal, V., Cook, W.: Finding cuts in the TSP (a preliminary report). Technical Report 95-05, DIMACS, Rutgers University, New Brunswick, NJ
2. Aardal, K., Weismantel, R.: Polyhedral combinatorics. In: M. Dell'Amico, F. Maffioli, S. Martello (eds.) Annotated Bibliographies in Combinatorial Optimization. pp. 31-44. New York, Wiley
3. 5. Oper. Res. Lett. 2, 107-111 (1983)
4. Barahona, F., Grötschel, M.:Onthe cycle polytopeofabinarymatroid.J. Comb.Th. (B).40, 40-62 (1986)
5. 2 }-Chvátal-Gomory cuts. Math. Program. 74, 221-235 (1996)
6. Caprara, A., Fischetti, M., Letchford, A.N.: On the separation of maximally violated mod-k cuts. Math. Program. 87, 37-56 (2000)
7. Caprara, A., Letchford, A.N.: On the separation of split cuts and related inequalities. Math. Program. 94, 279-294 (2003)
8. Chen, D.S., Zionts, S.: Comparison of some algorithms for solving the group theoretic programming problem. Oper. Res. 24, 1120-1128 (1976)
9. Chvátal, V.: Edmonds polytopes and a hierarchy of combinatorial problems. Discr. Math. 4, 305-337 (1973)
10. Chvátal, V., Cook, W., Hartmann, M.: On cutting-plane proofs in combinatorial optimization. Lin. Alg. Appl. 114(115), 455-499 (1989)
11. Cornuéjols, G., Guenin, B.: Ideal binary clutters, connectivity, and a conjecture of Seymour. SIAM J. Discr. Math. 15, 329-352 (2002)
12. Cornuéjols, G., Li, Y.: Elementary closures for integer programs. Oper. Res. Letts 28, 1-8 (2001)
13. Edmonds, J., Johnson, E.L.: Matching, Euler tours and the Chinese postman. Math. Program. 5, 88-124 (1973)
14. Gastou, G., Johnson, E.L.: Binary group and chinese postman polyhedra. Math. Program. 34, 1-33 (1986)
15. Gomory, R.E.: On the relation between integer and non-integer solutions to linear programs. Proc. Nat. Acad. Sci., 53, 260-265 (1965)
16. Gomory, R.E.: Some polyhedra related to combinatorial problems. Lin. Alg. Appl. 2, 451-558 (1969)
17. Grötschel, M., Pulleyblank, W.R.: Weakly bipartite graphs. Oper. Res. Lett. 1, 23-27 (1981)
18. Grötschel, M., Lovász, L., Schrijver, A.J.: Geometric Algorithms and Combinatorial Optimization. Wiley: New York, 1988
19. Grötschel, M., Padberg, M.W.: On the symmetric travelling salesman problem I: inequalities. Math. Program. 16, 265-280 (1979)
20. Grötschel, M., Truemper, K.: Decomposition and optimization over cycles in binary matroids. J. Comb. Th. (B) 46, 306-337 (1989)
21. Guenin, B.: A characterization of weakly bipartite graphs. J. Comb. Th. (B) 83, 112-168 (2001)
22. Letchford, A.N.: Separating a superclass of comb inequalities in planar graphs. Math. Oper. Res. 25, 443-454 (2000)
23. Letchford, A.N., Lodi, A.: Polynomial-time separation of simple comb inequalities. In: W.J. Cook, A.S. Schulz (Eds.), Integer Programming and Combinatorial Optimization 9. Lecture Notes in Computer Science 2337, Springer-Verlag, Berlin/Heidelberg, 2002, pp. 96-111
24. Naddef, D.: Polyhedral theory and branch-and-cut algorithms for the symmetric TSP. In: G. Gutin, A. Punnen (eds.), The Traveling Salesman Problem and its Variations. Kluwer Academic Publishers, 2002
25. Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley: New York, 1988
26. Oxley, J.G.: Matroid Theory. Oxford Science Publications: Oxford, 1992
27. Padberg, M.W., Grötschel, M.: Polyhedral computations. In: E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, D.B. Schmoys (Eds.) The Traveling Salesman Problem. John Wiley & Sons, Chichester, 1985
28. Padberg, M.W., Rao, M.R.: Odd minimum cut-sets and b-matchings. Math. Oper. Res. 7, 67-80 (1982)
29. Seymour, P.D.: The matroids with the max-flow min-cut property. J. Comb. Th. (B) 23, 189-222 (1977)
30. Seymour, P.D.: Decomposition of regular matroids. J. Comb. Th. (B) 28, 305-359 (1980)
31. Seymour, P.D.: Matroids and multicommodity flows. Eur. J. Comb. 2, 257-290 (1981)
32. Truemper, K.: Max-flow min-cut matroids: polynomial testing and polynomial algorithms for maximum flow and shortest routes. Math. Oper. Res. 12, 72-96 (1987)
33. Truemper, K.: A decomposition theory for matroids. IV: Decomposition of graphs. J. Comb. Th. (B) 45, 259-292 (1988)
34. Truemper, K.: Matroid Decomposition. Academic Press: San Diego, 1992