Pruning by isomorphism in branch-and-cut

Mathematical Programming, Series B

Volumn 94, Issue 1, 2002, Pages 71-90

  Margot, François ^a  

^a UNIVERSITY OF KENTUCKY   (United States)

Author keywords

Branch and cut; Isomorphism pruning; Symmetry

Indexed keywords

INTEGER LINEAR PROGRAMS; ISOMORPHISM PRUNING; SCHREIER-SIMS TABLE;

ERROR CORRECTION; LINEAR ALGEBRA; PROBLEM SOLVING; SET THEORY;

INTEGER PROGRAMMING;

EID: 33750972607     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-002-0358-2     Document Type: Article

References (38)

1. Avis, D.: A note on some computationally difficult set covering problems. Math. Prog. 8, 138-145 (1980)
2. Babai, L., Luks, E.M., Seress, Á.: Fast management of permutation groups I. SIAM J. Comp. 26, 1310-1342 (1997)
3. Brown, C.A., Finkelstein, L., Purdom, P.W.: A new base change algorithm for permutation groups. SIAM J. Comp. 18, 1037-1047 (1989)
4. Butler, G.: Computing in permutation and matrix groups II: Backtrack algorithm. Math. Comput. 39, 671-680 (1982)
5. Butler, G.: Fundamental Algorithms for Permutation Groups, Lecture Notes in Computer Science 559, Springer, 1991
6. Butler, G., Cannon, J.J.: Computing in permutation and matrix groups I: Normal closure, commutator subgroups, series. Math. Comp. 39, 663-670 (1982)
7. Butler, G., Lam, W.H.: A general backtrack algorithm for the isomorphism problem of combinatorial objects. J. Symbolic Comput. 1, 363-381 (1985)
8. Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices and Groups, Springer, 1993
9. ILOG CPLEX 7.1 User's Manual, 2001
10. Elf, M., Gutwenger, C., Jünger, M., Rinaldi, G.: Branch-and-cut algorithms for combinatorial optimization and their implementation in ABACUS. In: Jünger, M., Naddef, D., (eds). Lecture Notes in Computer Science 2241, Springer, pp. 155-222, 2001
11. Etzion, T., Wei, V., Zhang, Z.: Bounds on the sizes of constant weight covering codes. Designs, Codes and Cryptography 5, 217-239 (1995)
12. Feo, T.A., Resende, G.C.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Letters 8, 67-71 (1989)
13. Fulkerson, D.R., Nemhauser, G.L., Trotter, L.E.: Two computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of steiner triple systems. Math. Program. Study 2, 72-81 (1974)
14. Gibbons, P.B.: Computational methods in design theory. In: The CRC Handbook of Combinatorial Designs, Colbourn, C.J., Dinitz, J.H., (eds), CRC Press, pp. 718-740, 1996
15. Hall, M.: Combinatorial Theory, Wiley 1986
16. Hoffman, C.M.: Group-Theoretic Algorithms and Graph Isomorphism, Lecture Notes in Computer Science 136, Springer, 1982
17. Ivanov, A.V.: Constructive enumeration of incidence systems. Ann. Dis. Math. 26, 227-246 (1985)
18. Jerrum, M.: A compact representation for permutation groups. J. Algorithms 7, 60-78 (1986)
19. Jünger, M., Thienel, S.: Introduction to ABACUS - A branch-and-cut system. Oper. Res. Letters 22, 83-95 (1998)
20. Kreher, D.L., Stinson, D.R.: Combinatorial Algorithms, Generation, Enumeration, and Search, CRC Press, 1999
21. Leon, J.S.: On an algorithm for finding a base and a strong generating set for a group given by generating permutations. Math. Comput. 35, 941-974 (1980)
22. Leon, J.S.: Computing automorphism groups of combinatorial Objects. In: Computational Group Theory, Atkinson, M.D. (ed.), Academic Press, pp. 321-335, 1984
23. Luetolf, C., Margot, F.: A Catalog of minimally nonideal matrices. Math. Meth. Oper. Res. 47, 221-241 (1998)
24. Luks, E.: Permutation groups and polynomial-time computation. In: DIMACS Series in Discrete mathematics and Theoretical Computer Science 11, Groups and Computation, L. Finkelsein, W. Kantor (eds), pp. 139-175, 1993
25. Lytsin, S.: An updated table of the best binary codes known. In: Handbook of Coding Theory, V.S. Pless, W.C. Huffmann (eds), North-Holland, Elsevier, 1998
26. Mannino, C., Sassano, A.: Solving hard set covering problems. Oper. Res. Letters 18, 1-5 (1995)
27. Margot, F.: Small covering designs by branch-and-cut. To appear in Math. Program.
28. http://www.ms.uky.edu/~fmargot
29. McKay, D.: Isomorph-free exhaustive generation. J. Algorithms 26, 306-324 (1998)
30. Mills, W.H., Mullin, R.C.: Coverings and Packings. In: Contemporary Design Theory: A collection of Surveys, Dinitz, J.H., Stinson, D.R., (eds), Wiley, pp. 371-399, 1992
31. McKay, B.D.: Nauty user's guide (Version 1.5). Computer Science Department, Australian National University, Canberra
32. http://www.oreas.de
33. Padberg, M.W., Rinaldi, G.: A branch-and-cut algorithm for the resolution of large scale symmetric travelling salesman problems. SIAM Review 33, 60-100 (1991)
34. Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Ann. Dis. Math. 2, 107-120 (1978)
35. 10 minus a one-factor. Ars Combinatorica 21, 145-161 (1986)
36. Seress, A.: Nearly linear time algorithms for permutation groups: An interplay between theory and practice. Acta Applicandae Mathematicae 52, 183-207 (1998)
37. Thienel, S.: ABACUS - A branch-and-cut system. Ph.D. Thesis, Universität zu Köln 1995
38. Wolsey, L.A.: Integer Programming, Wiley 1998