Deterministic Õ(nm) time edge-splitting in undirected graphs

Journal of Combinatorial Optimization

Volumn 1, Issue 1, 1997, Pages 5-46

  Nagamochi, Hiroshi ^a   Ibaraki, Toshihide ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003220360     PISSN: 13826905     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009739202898     Document Type: Article

References (23)

1. 3) time," Proc. 26th ACM Symp. on Theory of Comput., 1994, pp. 658-667.
2. Benczúr A., "A representation of cuts within 6/5 times the edge connectivity with applications," Proc. 36th IEEE Symp. Found. Comp. Sci., 1995, pp. 92-102.
3. Bienstock, D. and Günlük, O., "A degree sequence problem related to network design," Networks, Vol.24, 1994, pp. 195-205.
4. Cai, G.-R. and Sun, Y.-G., "The minimum augmentation of any graph to k-edge-connected graph," Networks, Vol.19, 1989, pp. 151-172.
5. Frank, A., "Augmenting graphs to meet edge-connectivity requirements," SIAM J. Disc. Math., Vol.5, 1992, pp. 25-53.
6. Frank, A., " On the edge-connectivity algorithm of Nagamochi and Ibaraki," Laboratoire Artemis, IMAG, Université J. Fourier, Grenoble, March 1994.
7. Frank, A., Ibaraki, T. and Nagamochi, H., "On sparse subgraphs preserving connectivity properties," J. Graph Theory, Vol.17, 1993, pp. 275-281.
8. Gabow, H. N., "Applications of a poset representation to edge connectivity and graph rigidity," Proc. 32nd IEEE Symp. Found. Comp. Sci., Puerto Rico, 1991, pp. 812-821.
9. Gabow, H. N., "Efficient splitting off algorithms for graphs," Proc. 26th ACM Symp. on Theory of Comput., 1994, pp. 696-705.
10. Gomory, R. and Hu, T., "Multi-terminal network flows," SIAM J. on Applied Mathematics, Vol.9, 1961, pp. 551-570.
11. Goldberg , A. and Tarjan, R., "A new approach to the maximum flow problem," J. ACM, Vol.35, 1988, pp. 921-940.
12. Jackson, B., "Some remarks on arc-connectivity, vertex splitting, and orientation in graphs and digraphs," J. Graph Theory, Vol.12, 1988, pp. 429-436.
13. Lovász, L., Combinatorial Problems and Exercises, North-Holland 1979.
14. Mao-cheng, C. and Fleischner, H., "An Eulerian trail traversing specified edges in given order," J. Graph Theory, Vol.19, 1995, pp. 137-144.
15. Nagamochi, H. and Ibaraki, T., "A linear-time algorithm for finding a sparse k-connected spanning subgraph of a k-connected graph," Algorithmica, Vol.7, 1992, pp. 583-596.
16. Nagamochi, H. and Ibaraki, T., "Computing edge-connectivity of multigraphs and capacitated graphs," SIAM J. Disc. Math., Vol.5, 1992, pp. 54-66.
17. Nagamochi, H., Ono, T. and Ibaraki, T., "Implementing an efficient minimum capacity cut algorithm," Math. Prog., Vol.67, 1994, pp. 325-341.
18. Nagamochi, H., Nishimura, K. and Ibaraki, T., "Computing all small cuts in undirected networks," Lectures Notes in Computer Science 834, Springer-Verlag, Ding-Zhu Du and Xiang-Sun Zhang (Eds.), Algorithms and Computation, 5th International Symposium, ISAAC'94 Beijin, Aug. 1994, pp. 190-198.
19. Nagamochi, H. and Ibaraki, T., "A faster edge splitting algorithm in multigraphs and its application to the edge-connectivity augmentation problem," Lectures Notes in Computer Science 920, Springer-Verlag, Egon Balas and Jens Clausen (Eds.), 4th Integer Programming and Combinatoric Optimization, IPCO'95 Copenhagen, May 1995, pp. 401-413.
20. Nagamochi, H. and Ibaraki, T., "A simple and constructive proof of a minimum cut algorithm," Technical Report #96001, Kyoto University, Department of Applied Mathematics and Physics, 1996.
21. Nash-Williams, C. St. J. A., "On orientations, connectivity and odd vertex pairings in finite graphs," Canadian J. Math., Vol.12, 1960, pp. 555-567.
22. Stoer, M. and Wagner, F., "A simple min cut algorithm," Lecture Notes in Computer Science 855, Springer-Verlag, the Second Annual European Symposium on Algorithm, Utrecht, the Netherlands, September 1994, pp. 141-147.
23. Watanabe, T. and Nakamura, A., "Edge-connectivity augmentation problems," J. Comp. System Sci., Vol.35, 1987, pp. 96-144.