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arXiv · 2504.06033

Parallel Small Vertex Connectivity in Near-Linear Work and Polylogarithmic Depth

Yonggang Jiang·Changki Yun
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Abstract

We present a randomized parallel algorithm in the {\sf PRAM} model for $k$-vertex connectivity. Given an undirected simple graph, our algorithm either finds a set of fewer than $k$ vertices whose removal disconnects the graph or reports that no such set exists. The algorithm runs in $O(m \cdot \text{poly}(k, \log n))$ work and $O(\text{poly}(k, \log n))$ depth, which is nearly optimal for any $k = \text{poly}(\log n)$. Prior to our work, algorithms with near-linear work and polylogarithmic depth were known only for $k=3$ [Miller, Ramachandran, STOC'87]; for $k=4$, sequential algorithms achieving near-linear time were known [Forster, Nanongkai, Yang, Saranurak, Yingchareonthawornchai, SODA'20], but no algorithm with near-linear work could achieve even sublinear (on $n$) depth.

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Yonggang Jiang, Changki Yun. 2025-04-08. Parallel Small Vertex Connectivity in Near-Linear Work and Polylogarithmic Depth. https://arxiv.org/abs/2504.06033

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