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arXiv · 2109.13457

On the Geometry of Stable Steiner Tree Instances

James Freitag·Neshat Mohammadi·Aditya Potukuchi·Lev Reyzin
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Abstract

In this note we consider the Steiner tree problem under Bilu-Linial stability. We give strong geometric structural properties that need to be satisfied by stable instances. We then make use of, and strengthen, these geometric properties to show that $1.562$-stable instances of Euclidean Steiner trees are polynomial-time solvable. We also provide a connection between certain approximation algorithms and Bilu-Linial stability for Steiner trees.

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James Freitag, Neshat Mohammadi, Aditya Potukuchi, Lev Reyzin. 2021-09-28. On the Geometry of Stable Steiner Tree Instances. https://arxiv.org/abs/2109.13457

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