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arXiv · 1804.02242

Improved Approximation for Tree Augmentation: Saving by Rewiring

Fabrizio Grandoni·Christos Kalaitzis·Rico Zenklusen
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Abstract

The Tree Augmentation Problem (TAP) is a fundamental network design problem in which we are given a tree and a set of additional edges, also called \emph{links}. The task is to find a set of links, of minimum size, whose addition to the tree leads to a $2$-edge-connected graph. A long line of results on TAP culminated in the previously best known approximation guarantee of $1.5$ achieved by a combinatorial approach due to Kortsarz and Nutov [ACM Transactions on Algorithms 2016], and also by an SDP-based approach by Cheriyan and Gao [Algorithmica 2017]. Moreover, an elegant LP-based $(1.5+\epsilon)$-approximation has also been found very recently by Fiorini, Gro\ss, K\"onemann, and Sanit\'a [SODA 2018]. In this paper, we show that an approximation factor below $1.5$ can be achieved, by presenting a $1.458$-approximation that is based on several new techniques.

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Fabrizio Grandoni, Christos Kalaitzis, Rico Zenklusen. 2018-04-06. Improved Approximation for Tree Augmentation: Saving by Rewiring. https://arxiv.org/abs/1804.02242

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