Engineering Nearly Linear-time Algorithms for Small Vertex Connectivity

Vertex connectivity is a well-studied concept in graph theory with numerous applications. A k -connected if it remains connected after removing any −1 vertices. The vertex of the maximum such that -connected. There long history algorithmic development for efficiently computing connectivity. Recently, two near linear-time algorithms small were introduced by Forster et al. [SODA 2020]. Prior to that, best-known algorithm was one Henzinger [FOCS 1996] quadratic running time when small. In this article, we study practical performance addition, introduce new heuristic on key subroutine called local cut detection, which call degree counting. We prove improves space-efficiency (which can be good caching purposes) and allows terminate earlier. According experimental results random graphs planted cuts, hyperbolic graphs, real-world between 4 8, counting offers factor 2–4 speedup over original non-degree version almost 20 times some millions edges. It also outperforms previous state-of-the-art al., even relatively graphs.