Abstract
This paper addresses two augmentation problems related to bipartite graphs. The first, a fundamental graph-theoretical problem, is how to add a set of edges with the smallest possible cardinality so that the resulting graph is 2-edge-connected, i.e., bridge-connected, and still bipartite. The second problem, which arises naturally from research on the security of statistical data, is how to add edges so that the resulting graph is simple and dose not contain any bridges.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Adam, N.R., Wortmann, J.C.: Security-control methods for statistical database: A comparative study. ACM Computing Surveys 21, 515–556 (1989)
Cox, L.H.: Suppression methodology and statistical disclosure control. Journal of the American Statistical Association 75, 377–385 (1980)
Denning, D.E., Schlörer, J.: Inference controls for statistical databases. IEEE Computer 16, 69–82 (1983)
Eswaran, K.P., Tarjan, R.E.: Augmentation problems. SIAM Journal on Computing 5, 653–665 (1976)
Frank, A.: Connectivity augmentation problems in network design. In: Birge, J.R., Murty, K.G. (eds.) Mathematical Programming: State of the Art 1994, pp. 34–63. The University of Michigan (1994)
Gusfield, D.: A graph theoretic approach to statistical data security. SIAM Journal on Computing 17, 552–571 (1988)
Hsu, T.-s.: Graph Augmentation and Related Problems: Theory and Practice. PhD thesis, University of Texas at Austin (1993)
Hsu, T.-s., Kao, M.Y.: Security problems for statistical databases with general cell suppressions. In: Proceedings of the 9th International Conference on Scientific and Statistical Database Management, pp. 155–164 (1997)
Hsu, T.-s., Kao, M.Y.: Optimal augmentation for bipartite componentwise biconnectivity in linear time. SIAM Journal on Discrete Mathematics 19(2), 345–362 (2005)
Huang, P.-C., Wei, H.-W., Lu, W.-C., Shih, W.-K., Hsu, T.-s.: Smallest bipartite bridge-connectivity augmentation. Technical Report TR-IIS-06-016, Institute of Information Science, Academia Sinica, Nankang, Taipei, Taiwan (2006)
Jensen, J.B., Gabow, H.N., Jordán, T., Szigeti, Z.: Edge-connectivity augmentation with partition constraints. SIAM Journal on Discrete Mathematics 12, 160–207 (1999)
Kao, M.Y.: Linear-time optimal augmentation for componentwise bipartite-completeness of graphs. Information Processing Letters, 59–63 (1995)
Kao, M.Y.: Data security equals graph connectivity. SIAM Journal on Discrete Mathematics 9, 87–100 (1996)
Kao, M.Y.: Total protection of analytic-invariant information in cross-tabulated tables. SIAM Journal on Computing 26, 231–242 (1997)
Kelly, J.P., Golden, B.L., Assad, A.A.: Cell suppression: Disclosure protection for sensitive tabular data. Networks 22, 397–417 (1992)
Malvestuto, F.M., Moscarini, M.: Censoring statistical tables to protect sensitive information: Easy and hard problems. In: Proceedings of the 8th International Conference on Scientific and Statistical Database management, pp. 12–21 (1996)
Malvestuto, F.M., Moscarini, M.: Suppressing marginal totals from a two-dimensional table to protect sensitive information. Statistics and Computing 7, 101–114 (1997)
Malvestuto, F.M., Moscarini, M., Rafanelli, M.: Suppressing marginal cells to protect sensitive information in a two-dimensional statistical table. In: Proceedings of the 10th ACM SIGACT-SIGMOD-SIGACT Symposium on Principles of Database Systems, pp. 252–258 (1991)
Nagamochi, H.: Recent development of graph connectivity augmentation algorithms. IEICE Transactions on Information and System E83-D, 372–383 (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Huang, PC., Wei, HW., Lu, WC., Shih, WK., Hsu, Ts. (2007). Smallest Bipartite Bridge-Connectivity Augmentation (Extended Abstract). In: Kao, MY., Li, XY. (eds) Algorithmic Aspects in Information and Management. AAIM 2007. Lecture Notes in Computer Science, vol 4508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72870-2_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-72870-2_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72868-9
Online ISBN: 978-3-540-72870-2
eBook Packages: Computer ScienceComputer Science (R0)