Steiner point removal with distortion O(log k)

Arnold Filtser

doi:10.1137/1.9781611975031.90

Steiner point removal with distortion O(log k)

Arnold Filtser

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

12 Scopus citations

Abstract

In the Steiner point removal (SPR) problem, we are given a weighted graph G = (V;E) and a set of terminals K § V of size k. The objective is to find a minor M of G with only the terminals as its vertex set, such that the distance between the terminals will be preserved up to a small multiplicative distortion. Kamma, Krauthgamer and Nguyen [KKN15] used a ball-growing algorithm with exponential distributions to show that the distortion is at most O(log5 k). Cheung [Che18] improved the analysis of the same algorithm, bounding the distortion by O(log2 k). We improve the analysis of this ball-growing algorithm even further, bounding the distortion by O(log k).

Original language	English
Title of host publication	29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Editors	Artur Czumaj
Publisher	Association for Computing Machinery
Pages	1361-1373
Number of pages	13
ISBN (Electronic)	9781611975031
DOIs	https://doi.org/10.1137/1.9781611975031.90
State	Published - 1 Jan 2018
Event	29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States Duration: 7 Jan 2018 → 10 Jan 2018

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference	29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Country/Territory	United States
City	New Orleans
Period	7/01/18 → 10/01/18

ASJC Scopus subject areas

Software
General Mathematics

Access to Document

10.1137/1.9781611975031.90

Cite this

@inproceedings{5e6e5b1d9d034073a043993fd6e888bf,

title = "Steiner point removal with distortion O(log k)",

abstract = "In the Steiner point removal (SPR) problem, we are given a weighted graph G = (V;E) and a set of terminals K § V of size k. The objective is to find a minor M of G with only the terminals as its vertex set, such that the distance between the terminals will be preserved up to a small multiplicative distortion. Kamma, Krauthgamer and Nguyen [KKN15] used a ball-growing algorithm with exponential distributions to show that the distortion is at most O(log5 k). Cheung [Che18] improved the analysis of the same algorithm, bounding the distortion by O(log2 k). We improve the analysis of this ball-growing algorithm even further, bounding the distortion by O(log k).",

author = "Arnold Filtser",

year = "2018",

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doi = "10.1137/1.9781611975031.90",

language = "English",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "Association for Computing Machinery",

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}

Filtser, A 2018, Steiner point removal with distortion O(log k). in A Czumaj (ed.), 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery, pp. 1361-1373, 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, United States, 7/01/18. https://doi.org/10.1137/1.9781611975031.90

Steiner point removal with distortion O(log k). / Filtser, Arnold.
29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. ed. / Artur Czumaj. Association for Computing Machinery, 2018. p. 1361-1373 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In the Steiner point removal (SPR) problem, we are given a weighted graph G = (V;E) and a set of terminals K § V of size k. The objective is to find a minor M of G with only the terminals as its vertex set, such that the distance between the terminals will be preserved up to a small multiplicative distortion. Kamma, Krauthgamer and Nguyen [KKN15] used a ball-growing algorithm with exponential distributions to show that the distortion is at most O(log5 k). Cheung [Che18] improved the analysis of the same algorithm, bounding the distortion by O(log2 k). We improve the analysis of this ball-growing algorithm even further, bounding the distortion by O(log k).

AB - In the Steiner point removal (SPR) problem, we are given a weighted graph G = (V;E) and a set of terminals K § V of size k. The objective is to find a minor M of G with only the terminals as its vertex set, such that the distance between the terminals will be preserved up to a small multiplicative distortion. Kamma, Krauthgamer and Nguyen [KKN15] used a ball-growing algorithm with exponential distributions to show that the distortion is at most O(log5 k). Cheung [Che18] improved the analysis of the same algorithm, bounding the distortion by O(log2 k). We improve the analysis of this ball-growing algorithm even further, bounding the distortion by O(log k).

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M3 - Conference contribution

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BT - 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018

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T2 - 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018

Y2 - 7 January 2018 through 10 January 2018

ER -

Steiner point removal with distortion O(log k)

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