Optimal Augmentation for Bipartite Componentwise Biconnectivity in Linear Time

A graph is componentwise biconnected if every connected component either is an isolated vertex or is biconnected. We present a linear-time algorithm for the problem of adding the smallest number of edges to make a bipartite graph componentwise biconnected while preserving its bipartiteness. This algorithm has immediate applications for protecting sensitive information in statistical tables.Comment: A preliminary version appeared in T. Asano, Y. Igarashi, H. Nagamochi, S. Miyano, and S. Suri, editors, Lecture Notes in Computer Science 1178: Proceedings of the 7th Annual International Symposium on Algorithms and Computation, pages 213--222. Springer-Verlag, New York, NY, 199