[2311.17010] Node Connectivity Augmentation of Highly Connected Graphs
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Computer Science > Data Structures and Algorithms

arXiv:2311.17010 (cs)
[Submitted on 28 Nov 2023]

Title:Node Connectivity Augmentation of Highly Connected Graphs

Authors:Waldo Galvez, Dylan Hyatt-Denesik, Afrouz Jabal Ameli, Laura Sanita
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Abstract: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 $\frac{3}{2}$-approximation algorithm for the weighted setting, and a $\frac{4}{3}$-approximation algorithm for the unweighted setting.
Subjects: Data Structures and Algorithms (cs.DS)
Cite as: arXiv:2311.17010 [cs.DS]
  (or arXiv:2311.17010v1 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.2311.17010

Submission history

From: Dylan Hyatt-Denesik [view email]
[v1] Tue, 28 Nov 2023 18:04:17 UTC (90 KB)
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