Node-connectivity augmentation is a fundamental network design problem. We are given a k-node connected graph G together with an additional set of links, and the goal is to add a cheap subset of links to G to make it (k+1)-node connected. In this work, we characterize completely the computational complexity status of the problem, by showing hardness for all values of k which were not addressed previously in the literature. We then focus on k-node connectivity augmentation for k=n−4, which corresponds to the highest value of k for which the problem is NP-hard. We improve over the previously best known approximation bounds for this problem, by developing a 23-approximation algorithm for the weighted setting, and a 34-approximation algorithm for the unweighted setting.
@article{arxiv.2311.17010,
title = {Node Connectivity Augmentation of Highly Connected Graphs},
author = {Waldo Galvez and Dylan Hyatt-Denesik and Afrouz Jabal Ameli and Laura Sanita},
journal= {arXiv preprint arXiv:2311.17010},
year = {2023}
}