Computing and Testing Small Vertex Connectivity in Near-Linear Time and Queries

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We present a new, simple, algorithm for the local vertex connectivity problem (LocalVC) introduced by Nanongkai~et~al. [STOC'19]. Roughly, given an undirected unweighted graph $G$, a seed vertex $x$, a target volume $\nu$, and a target separator size $k$, the goal of LocalVC is to remove $k$ vertices `near' $x$ (in terms of $\nu$) to di...More