## A Note on the Computational Complexity of Unsmoothened Vertex Attack Tolerance

28 Mar 2016  ·  Ercal Gunes ·

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...

PDF Abstract

# Code Add Remove Mark official

No code implementations yet. Submit your code now

# Categories

Computational Complexity Discrete Mathematics

# Datasets

Add Datasets introduced or used in this paper