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On the Geometry of Stable Steiner Tree Instances

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James Freitag, Neshat Mohammadi, Aditya Potukuchi, Lev Reyzin

Data Structures and Algorithms · Submitted 28 Sep 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID2109.13457 (version 1)
Pith IDNGRYIJJW, Pith's permanent record of this paper and its review
CitationAditya Potukuchi, James Freitag, Lev Reyzin, Neshat Mohammadi. "On the Geometry of Stable Steiner Tree Instances." arXiv:2109.13457 (2021). https://pith.science/paper/NGRYIJJW
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,501 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.02 · states quantitative result 0.98 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this note we consider the Steiner tree problem under Bilu-Linial stability. background 0.75 0.61 0.03 asserted 0.68
s1 We give strong geometric structural properties that need to be satisfied by stable instances. contribution 0.70 0.93 0.09 asserted 1.00
s2 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. result 0.97 0.94 0.78 asserted 1.00
s3 We also provide a connection between certain approximation algorithms and Bilu-Linial stability for Steiner trees. contribution 0.77 0.87 0.05 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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