Durand de Gevigney and Szigeti \cite{DgGSz} have recently given a min-max theorem for the (2,k)-connectivity augmentation problem. This article provides an O(n3(m+nlogn)) algorithm to find an optimal solution for this problem.
Cite
@article{arxiv.2004.08645,
title = {The $(2,k)$-connectivity augmentation problem: Algorithmic aspects},
author = {Florian Hörsch and Zoltán Szigeti},
journal= {arXiv preprint arXiv:2004.08645},
year = {2021}
}