Breaching the 2-approximation barrier for the forest augmentation problem
@article{Grandoni2021BreachingT2, title={Breaching the 2-approximation barrier for the forest augmentation problem}, author={Fabrizio Grandoni and Afrouz Jabal Ameli and Vera Traub}, journal={Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing}, year={2021} }
The basic goal of survivable network design is to build cheap networks that guarantee the connectivity of certain pairs of nodes despite the failure of a few edges or nodes. A celebrated result by Jain [Combinatorica'01] provides a 2-approximation for a wide class of these problems. However nothing better is known even for very basic special cases, raising the natural question whether any improved approximation factor is possible at all. In this paper we address one of the most basic problems…
6 Citations
A $(1.5+\epsilon)$-Approximation Algorithm for Weighted Connectivity Augmentation
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A well-chosen local search algorithm is designed for WCAP, and it is proved that an optimum solution can be decomposed into smaller components, at least one of which leads to a good local search step as long as the claimed approximation guarantee is achieved.
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We give an almost-linear time algorithm for the Steiner connectivity augmentation problem: given an undirected graph, find a smallest (or minimum weight) set of edges whose addition makes a given set…
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This paper gives a $(1.3+\varepsilon)-approximation algorithm for 2-ECSS, where $\varpsilon$ is an arbitrary positive fixed constant, which improves the previously known best approximation ratio.
Matching Augmentation via Simultaneous Contractions
- Mathematics, Computer ScienceArXiv
- 2022
A polynomial-time algorithm with an approximation ratio of $13/8 = 1.625$ improving upon an earlier $5/3$-approximation, and introducing the technique of repeated simultaneous contractions to provide improved lower bounds for instances that cannot be contracted.
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