Biconnectivity in Linear Time

Title: Biconnectivity in Linear Time

Research Question: How can we efficiently determine the smallest set of edges to add to a bipartite graph to make it component-wise biconnected while preserving its bipartiteness?

Methodology: The researchers proposed a linear-time algorithm for the problem of adding the smallest number of edges to a bipartite graph to make it component-wise biconnected while maintaining its bipartiteness. This algorithm has immediate applications for protecting sensitive information in statistical tables.

Results: The algorithm provides an optimal solution to the problem by finding an optimal biconnector - a set of legal edges that, when added to the graph, makes it component-wise biconnected. The researchers proved an optimal bound on the smallest number of additional edges needed for the problem.

Implications: The linear-time algorithm developed by the researchers has significant implications for the field. It provides an efficient solution to the problem of adding edges to a bipartite graph to maintain its component-wise biconnectivity, which is particularly useful for protecting sensitive information in statistical tables. The algorithm's simplicity and efficiency make it widely applicable in various fields that require protecting sensitive data while maintaining the integrity of the information.

Link to Article: https://arxiv.org/abs/0102009v1 Authors: arXiv ID: 0102009v1