Detecting symmetries by branch &cut

Mathematical Programming

Volumn 98, Issue 1-3, 2003, Pages 369-384

  Buchheim, Christoph ^a   Jünger, Michael ^a  

^a UNIVERSITY OF COLOGNE   (Germany)

Author keywords

Branch cut; Integer programming; Symmetry

Indexed keywords

AUTOMORPHISM GROUPS; AUTOMORPHISMS; EXACT ALGORITHMS; GRAPH DRAWING; MATCHING POLYTOPE; POLYTOPES; SYMMETRY DETECTION; TRAVELING SALESMAN POLYTOPE;

COMPUTATIONAL COMPLEXITY; CRYSTAL SYMMETRY; DRAWING (GRAPHICS); INTEGER PROGRAMMING; TOPOLOGY;

ALGORITHMS;

EID: 18244366958     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-003-0409-3     Document Type: Conference Paper

References (27)

1. Abelson, D., Hong, S., Taylor, D.:A group-theoretic method for drawing graphs symmetrically. In: Goodrich, M., Kobourov, S. (eds)., Graph Drawing 2002, volume 2528 of Lecture Notes in Computer Science pp. 86-97, Springer-Verlag, 2002
2. Balas, E.: The asymmetric assignment problem and some new facets of the traveling salesman polytope on a directed graph. SIAM J. Discrete Math. 2, 425-451 (1989)
3. Balas, E., Fischetti, M.: A lifting procedure for the asymmetric traveling salesman polytope and a large class of new facets. Math. Program. 58, 325-352 (1993)
4. Balinski, M., Russakoff, A.: On the assignment polytope. SIAM Rev. 16, 516-525 (1974)
5. Benczúr, A., Fülöp, O.: Fast algorithms for even/odd minimum cuts and generalizations. In: ESA, pp. 88-99, (2000)
6. Birkhoff, G.: Tres observaciones sobre el algebra lineal. Revista Facultad de Ciencias Exactas, Puras y Applicadas Universidad Nacional de Tucuman Serie A (Matematicas y Fisica Teoretica) 5, 147-151 (1946)
7. Carr, H., Kocay, W.: An algorithm for drawing a graphy symmetrically. Bulletin of the ICA 27, 19-25 (1999)
8. Chen, H., Lu, H., Yen, H.: On Maximum Symmetric Subgraphs. In: Marks, J., (ed)., Graph Drawing 2000, volume 1984 of Lecture Notes in Computer Science, p. 372-383 Springer-Verlag, 2001
9. Eades, P., Lin, X.: Spring algorithms and symmetry. Theor. Comput. Sci. 240(2), 379-405 (2000)
10. Edmonds, J.: Paths, trees, and flowers. Can. J. Math. 17, 449-467 (1965)
11. de Fraysseix, H.:An heuristic for graph symmetry detection. In: Kratochvil, J., (ed)., Graph Drawing '99, volume 1731 of Lecture Notes in Computer Science, pp. 276-285. Springer-Verlag, 1999
12. Goemans, M., Ramakrishnan, V.: Minimizing submodular functions over families of sets. Combinatorica 15(4), 499-513 (1995)
13. Grötschel, M. Lovász, L., and Schrijver, A.: Geometric algorithms and combinatorial optimization. Springer-Verlag, 1988
14. Grötschel, M., Padberg, M.: Polyhedral theory. In: Lawler, E., Lenstra, J., Rinnooy Kan, A., Shmoys, D. (eds)., The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, pp. 251-305 John Wiley & Sons, 1985
15. Hardy, G., Wright, E.: An introduction to the theory of numbers. Clarendon Press, 1938
16. Hong, S., Eades, P.: Drawing Planar Graphs Symmetrically II: Biconnected graphs. CS-IVG-2001-01, University of Sydney 2001
17. Hong, S., Eades, P.: Drawing Planar Graphs Symmetrically III: Oneconnected Graphs. CS-IVG-2001-02, University of Sydney, 2001
18. Hong, S., Eades, P.: Drawing Planar Graphs Symmetrically IV: Disconnected Graphs. CS-IVG-2001-03, University of Sydney, 2001
19. Hong, S., McKay, B., Eades, P.: Symmetric drawings of triconnected planar graphs. SODA 2002, pp. 356-365, (2002)
20. Jünger, M., Thienel, S.:The ABACUS system for branch-and-cut-and- price-algorithms in integer programming and combinatorial optimization. Softw. Pract. Exper. 30(11), 1325-1352 (2000)
21. Klin, M., Rücker, C., Rücker, G., Tinhofer, G.: Algebraic combinatorics in mathematical chemistry. Methods and Algorithms. I. Permutation groups and coherent (cellular) algebras. Technische Universität München, Fakultät für Mathematik, 1995
22. Lubiw, A.: Some NP-Complete problems similar to graph isomorphism. SIAM J. Comput. 10(1), 11-21 (1981)
23. Manning, J.: Computational complexity of geometric symmetry detectionin graphs. In: Great Lakes Computer Science Conference, volume 507 of Lecture Notes in Computer Science, pp. 1-7. Springer-Verlag, 1990
24. McKay, B.: nauty user's guide. Tecmnical Report TR-CS-90-02, Computer Science Department, Australian National University, 1990
25. Padberg, M., Rao, M.: Odd minimum cut-sets and b-matchings. Math. Oper. Res. 7, 67-80 (1982)
26. Purchase, H.: Which aesthetic has the greatest effect on human understanding? In: Di Battista, G., (ed), Graphy Drawing '97, volume 1353 of Lecture Notes in Computer Science, pp. 248-261. Springer-Verlag, 1997
27. Read, R., Corneil, D.: The graph isomorphism disease. J. Graph Theory 1, 339-363 (1977)