# On the Geometry of Stable Steiner Tree Instances

@inproceedings{Freitag2021OnTG, title={On the Geometry of Stable Steiner Tree Instances}, author={James Freitag and Neshat Mohammadi and Aditya Potukuchi and L. Reyzin}, booktitle={Canadian Conference on Computational Geometry}, year={2021} }

In this work 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 . 59-stable instances of Euclidean Steiner trees are polynomial-time solvable by showing it reduces to the minimum spanning tree problem. We also provide a connection between certain approximation algorithms and Bilu-Linial stability for Steiner…

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