Abstract
Vertex connectivity is a classic graph-theoretic notion that roughly measures the robustness of a graph against node failures. A classic open problem, asked by Aho, Hopcroft and Ullman in 1975, is whether or not vertex connectivity can be computed in linear time. In this short talk, I will give a quick survey on exciting developments on fast vertex connectivity algorithms in the past few years (since 2019) that culminate in a celebrated "poly-log max-flows" algorithm, leading to an almost linear time vertex connectivity algorithm by a recent breakthrough in max-flow algorithm.