Optimal Augmentation for Bipartite Componentwise Biconnectivity in Linear Time

TL;DR

This paper introduces a linear-time algorithm to minimally augment bipartite graphs to be componentwise biconnected without losing bipartiteness, aiding in data privacy protection.

Contribution

It presents the first linear-time solution for bipartite componentwise biconnectivity augmentation that preserves bipartiteness.

Findings

Algorithm runs in linear time

Minimizes added edges for biconnectivity

Applicable to data privacy in statistical tables

Abstract

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.