Symmetric ILP: Coloring and small integers

Discrete Optimization

Volumn 4, Issue 1, 2007, Pages 40-62

  Margot, François ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Branch and cut; Isomorphism pruning; Symmetry

Indexed keywords

COLORING; INTEGER PROGRAMMING; PROBLEM SOLVING;

BINARY VARIABLES; BRANCH-AND-CUT; ISOMORPHISM PRUNING;

LINEAR PROGRAMMING;

EID: 33846593931     PISSN: 15725286     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disopt.2006.10.008     Document Type: Article

References (26)

1. D.A. Bulutoglu, F. Margot, Classification of orthogonal arrays by integer programming, 2005. Working paper
2. Butler G. Computing in permutation and matrix groups II: Backtrack algorithm. Mathematics of Computation 39 (1982) 671-680
3. Butler G. Fundamental Algorithms for Permutation Groups. Lecture Notes in Computer Science vol. 559 (1991), Springer
4. Butler G., and Cannon J.J. Computing in Permutation and matrix groups I: Normal closure, commutator subgroups, series. Mathematics of Computation 39 (1982) 663-670
5. Butler G., and Lam W.H. A general backtrack algorithm for the isomorphism problem of combinatorial objects. Journal of Symbolic Computation 1 (1985) 363-381
6. Chetwynd A.G., and Wilson R.J. The rise and fall of the critical graph conjecture. Journal of Graph Theory 7 (1983) 153-157
7. http://www.coin-or.org
8. M. Elf, C. Gutwenger, M. Jünger, G. Rinaldi, Branch-and-cut algorithms for combinatorial optimization and their implementation in ABACUS, pp. 155-222. In [10]
9. Hedayat A.S., Sloane N.J.A., and Stufken J. Orthogonal Arrays: Theory and Applications (1999), Springer
10. In: Jünger M., and Naddef D. (Eds). Computational Combinatorial Optimization. Lecture Notes in Computer Science vol. 2241 (2001), Springer
11. Holt D.F., Eick B., and O'Brien E.A. Handbook of Computational Group Theory (2004), Chapman & Hall/CRC
12. Hoffman C.M. Group-Theoretic Algorithms and Graph Isomorphism. Lecture Notes in Computer Science vol. 136 (1982), Springer
13. ILOG CPLEX 9.0 User's Manual, 2003
14. Kreher D.L., and Stinson D.R. Combinatorial Algorithms, Generation, Enumeration, and Search (1999), CRC Press
15. Leon J.S. On an algorithm for finding a base and a strong generating set for a group given by generating permutations. Mathematics of Computation 35 (1980) 941-974
16. Leon J.S. Computing automorphism groups of combinatorial objects. In: Atkinson M.D. (Ed). Computational Group Theory (1984), Academic Press 321-335
17. http://wpweb2.tepper.cmu.edu/fmargot/index.html
18. Margot F. Pruning by isomorphism in branch-and-cut. Mathematical Programming 94 (2002) 71-90
19. Margot F. Exploiting orbits in symmetric ILP. Mathematical Programming. Series B 98 (2003) 3-21
20. McKay D. Isomorph-free exhaustive generation. Journal of Algorithms 26 (1998) 306-324
21. Meredith G.H.J. Regular n-valent n-connected nonHamiltonian non-n-edge-colorable graphs. Journal of Combinatorial Theory. Series B 14 (1973) 55-60
22. Owen J.H., and Mehrotra S. On the value of binary expansions for general mixed-integer linear programs. Operations Research 50 (2002) 810-819
23. Padberg M.W., and Rinaldi G. A branch-and-cut algorithm for the resolution of large scale symmetric travelling salesman problems. SIAM Review 33 (1991) 60-100
24. Vizing V.G. On an estimate of the chromatic class of a p-graph. Diskretnyǐ Analiz 3 (1964) 25-30
25. West D.B. Introduction to Graph Theory. 2nd edition (2001), Prentice Hall
26. Wolsey L.A. Integer Programming (1998), Wiley