A Unifying Augmentation Algorithm for Two-Edge Connectivity and Biconnectivity

Journal of Combinatorial Optimization

Volumn 2, Issue 3, 1998, Pages 237-256

  Hsu, Tsan Sheng ^a   Kao, Ming Yang ^b  

^a INSTITUTE OF INFORMATION SCIENCE   (Taiwan)

^b Yale University   (United States)

Author keywords

Bi level augmentation; Biconnectivity; Linear time algorithm; Two edge connectivity

Indexed keywords

EID: 0011523628     PISSN: 13826905     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009746026508     Document Type: Article

References (31)

1. B. Bollobás, Graph Theory: An Introductory Course, Springer-Verlag: New York, NY, 1979.
2. N. Christofides and C. A. Whitlock, "Network synthesis with connectivity constraints - a survey," in Proceedings of the 9th IFORS International Conference on Operational Research, 1981, pp. 705-723.
3. K. P. Eswaran and R. E. Tarjan, "Augmentation problems," SIAM Journal on Computing vol. 5, pp. 653-665, 1976.
4. A. Frank, "Augmenting graphs to meet edge-connectivity requirements," SIAM Journal on Discrete Mathematics vol. 5, pp. 25-43, 1992.
5. A. Frank, "Connectivity augmentation problems in network design," in J. R. Birge and K. G. Murty, editors, Mathematical Programming: State of the Art 1994, pp. 34-63. The University of Michigan, 1994.
6. H. Frank and W. Chou, "Connectivity considerations in the design of survivable networks," IEEE Transactions on Circuit Theory vol. CT-17, pp. 486-490, 1970.
7. D. Gusfield, "A graph theoretic approach to statistical data security," SIAM Journal on Computing vol. 17, pp. 552-571, 1988.
8. F. Harary, Graph Theory, Addison-Wesley: Reading, Massachusetts, 1969.
9. T.-s. Hsu, Graph Augmentation and Related Problems: Theory and Practice. PhD thesis, University of Texas at Austin, 1993.
10. T.-s. Hsu and M. Y. Kao, "Optimal augmentation for bipartite componentwise biconnectivity in linear time," in T. Asano, Y. Igarashi, H. Nagamochi, S. Miyano, and S. Suri, editors, Lecture Notes in Computer Science 1178: Proceedings of the 7th International Symposium on Algorithms and Computation, pp. 213-222. Springer-Verlag: New York, NY, 1996.
11. T.-s. Hsu and M. Y. Kao, "Security problems for statistical databases with general cell suppressions," in Proceedings of the 9th International Conference on Scientific and Statistical Database Management, 1997, pp. 155-164.
12. T.-s. Hsu and V. Ramachandran, "A linear time algorithm for triconnectivity augmentation," in Proceedings of the 32th Annual IEEE Symposium on Foundations of Computer Science, 1991, pp. 548-559.
13. T.-s. Hsu and V. Ramachandran, "On finding a smallest augmentation to biconnect a graph," SIAM Journal on Computing vol. 22, pp. 889-912, 1993.
14. S. P. Jain and K. Gopal, "On network augmentation," IEEE Transactions on Reliability vol. R-35, pp. 541-543, 1986.
15. G. Kant, Algorithms for Drawing Planar Graphs. PhD thesis, Utrecht University, the Netherlands, 1993.
16. M. Y. Kao, "Linear-time optimal augmentation for componentwise bipartite-completeness of graphs," Information Processing Letters, pp. 59-63, 1995.
17. M. Y. Kao, "Data security equals graph connectivity," SIAM Journal on Discrete Mathematics vol. 9, pp. 87-100, 1996.
18. M. Y. Kao, "Total protection of analytic-invariant information in cross-tabulated tables," SIAM Journal on Computing vol. 26, pp. 231-242, 1997.
19. J. A. La Poutré and J. Westbrook, "Dynamic two-connectivity with backtracking," in Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms, 1994, pp. 204-212.
20. F. M. Malvestuto and M. Moscarini, "Censoring statistical tables to protect sensitive information: Easy and hard problems," in Proceedings of the 8th International Conference on Scientific and Statistical Database management, 1996, pp. 12-21.
21. F. M. Malvestuto and M. Moscarini, "Suppressing marginal totals from a two-dimensional table to protect sensitive information," Statistics and Computing vol. 7, pp. 101-114, 1997.
22. F. M. Malvestuto, M. Moscarini, and M. Rafanelli, "Suppressing marginal cells to protect sensitive information in a two-dimensional statistical table," in Proceedings of the 3rd ACM Symposium on Principles of Database Systems, 1991, pp. 252-258.
23. M. Rauch, "Improved data structures for fully dynamic biconnectivity," in Proceedings of the 26th Annual ACM Symposium on Theory of Computing, 1994, pp. 686-695.
24. A. Rosenthal and A. Goldner, "Smallest augmentations to biconnect a graph," SIAM Journal on Computing vol. 6, pp. 55-66, 1977.
25. K. Steiglitz, P. Weiner, and D. J. Kleitman, "The design of minimum-cost survivable networks," IEEE Transactions on Circuit Theory vol. CT-16, pp. 455-460, 1969.
26. S. Taoka and T. Watanabe, "Minimum augmentation to k-edge-connect specified vertices of a graph," in D. Z. Du and X. S. Zhang, editors, Lecture Notes in Computer Science 834: Proceedings of the 5th Annual International Symposium on Algorithms and Computation, pp. 217-225, New York, NY, 1994. Springer-Verlag.
27. W. T. Tutte, Connectivity in Graphs, University of Toronto Press, 1966.
28. T. Watanabe, Y. Higashi, and A. Nakamura, "An approach to robust network construction from graph augmentation problems," in Proceedings of 1990 IEEE International Symposium on Circuits and Systems, 1990, pp. 2861-2864.
29. T. Watanabe, Y. Higashi, and A. Nakamura, "Graph augmentation problems for a specified set of vertices," in T. Asano, T. Ibaraki, H. Imai, and T. Nishizeki, editors, Lecture Notes in Computer Science 450: Proceedings of the 1st Annual International Symposium on Algorithms, pp. 378-387. Springer-Verlag: New York, NY, 1990.
30. T. Watanabe, S. Taoka, and T. Mashima, "Minimum-cost augmentation to 3-edge-connect all specified vertices in a graph," in Proceedings of 1993 IEEE International Symposium on Circuits and Systems, 1993, pp. 2311-2314.
31. J. Westbrook and R. E. Tarjan, "Maintaining bridge-connected and biconnected components on-line," Algorithmica, vol. 7, nos. 5/6, pp. 433-464, 1992.