A Note on the Computational Complexity of Unsmoothened Vertex Attack Tolerance

Gunes Ercal

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arXiv · 1603.08430

A Note on the Computational Complexity of Unsmoothened Vertex Attack Tolerance

Gunes Ercal

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Abstract

We have previously introduced vertex attack tolerance (VAT) and unsmoothened VAT (UVAT), denoted respectively as $\tau(G) = \min_{S \subset V} \frac{|S|}{|V-S-C_{max}(V-S)|+1}$ and $\hat{\tau}(G) = \min_{S \subset V} \frac{|S|}{|V-S-C_{max}(V-S)|}$, where $C_{max}(V-S)$ is the largest connected component in $V-S$, as appropriate mathematical measures of resilience in the face of targeted node attacks for arbitrary degree networks. Here we prove the hardness of approximating $\hat{\tau}$ under various plausible computational complexity hypotheses.

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Gunes Ercal. 2016-03-28. A Note on the Computational Complexity of Unsmoothened Vertex Attack Tolerance. https://arxiv.org/abs/1603.08430

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