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arXiv · 2111.02234

Approximation Algorithms for Vertex-Connectivity Augmentation on the Cycle

Waldo Gálvez·Francisco Sanhueza-Matamala·José A. Soto
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Abstract

Given a $k$-vertex-connected graph $G$ and a set $S$ of extra edges (links), the goal of the $k$-vertex-connectivity augmentation problem is to find a set $S' \subseteq S$ of minimum size such that adding $S'$ to $G$ makes it $(k+1)$-vertex-connected. Unlike the edge-connectivity augmentation problem, research for the vertex-connectivity version has been sparse. In this work we present the first polynomial time approximation algorithm that improves the known ratio of 2 for $2$-vertex-connectivity augmentation, for the case in which $G$ is a cycle. This is the first step for attacking the more general problem of augmenting a $2$-connected graph. Our algorithm is based on local search and attains an approximation ratio of $1.8704$. To derive it, we prove novel results on the structure of minimal solutions.

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Waldo Gálvez, Francisco Sanhueza-Matamala, José A. Soto. 2021-11-03. Approximation Algorithms for Vertex-Connectivity Augmentation on the Cycle. https://arxiv.org/abs/2111.02234

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