Near-linear time approximation schemes for Steiner tree and forest in low-dimensional spaces

Yair Bartal; Lee Ad Gottlieb

doi:10.1145/3406325.3451063

Near-linear time approximation schemes for Steiner tree and forest in low-dimensional spaces

Yair Bartal
, Lee Ad Gottlieb

The Rachel and Selim Benin School of Engineering and Computer Science

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

7 Scopus citations

Abstract

We give an algorithm that computes a (1+?)-approximate Steiner forest in near-linear time n · 2(1/?)O(ddim2) (loglogn)2, where ddim is the doubling dimension of the metric space. This improves upon the best previous result due to Chan et al. (SIAM J. Comput. 4 (2018)), who gave a runtime of about n2O(ddim) · 2(ddim/?)O(ddim) ?logn. For Steiner tree our methods achieve an even better runtime n (logn)(1/?)O(ddim2).

Original language	English
Title of host publication	STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
Editors	Samir Khuller, Virginia Vassilevska Williams
Publisher	Association for Computing Machinery
Pages	1028-1041
Number of pages	14
ISBN (Electronic)	9781450380539
DOIs	https://doi.org/10.1145/3406325.3451063
State	Published - 15 Jun 2021
Event	53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy Duration: 21 Jun 2021 → 25 Jun 2021

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)	0737-8017

Conference

Conference	53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Country/Territory	Italy
City	Virtual, Online
Period	21/06/21 → 25/06/21

Bibliographical note

Publisher Copyright:
© 2021 ACM.

Keywords

Steiner forest
banyans
doubling dimension

Access to Document

10.1145/3406325.3451063

Cite this

Bartal, Y., & Gottlieb, L. A. (2021). Near-linear time approximation schemes for Steiner tree and forest in low-dimensional spaces. In S. Khuller, & V. V. Williams (Eds.), STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing (pp. 1028-1041). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/3406325.3451063

Bartal, Yair ; Gottlieb, Lee Ad. / Near-linear time approximation schemes for Steiner tree and forest in low-dimensional spaces. STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. editor / Samir Khuller ; Virginia Vassilevska Williams. Association for Computing Machinery, 2021. pp. 1028-1041 (Proceedings of the Annual ACM Symposium on Theory of Computing).

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abstract = "We give an algorithm that computes a (1+?)-approximate Steiner forest in near-linear time n · 2(1/?)O(ddim2) (loglogn)2, where ddim is the doubling dimension of the metric space. This improves upon the best previous result due to Chan et al. (SIAM J. Comput. 4 (2018)), who gave a runtime of about n2O(ddim) · 2(ddim/?)O(ddim) ?logn. For Steiner tree our methods achieve an even better runtime n (logn)(1/?)O(ddim2).",

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Bartal, Y & Gottlieb, LA 2021, Near-linear time approximation schemes for Steiner tree and forest in low-dimensional spaces. in S Khuller & VV Williams (eds), STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 1028-1041, 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021, Virtual, Online, Italy, 21/06/21. https://doi.org/10.1145/3406325.3451063

Near-linear time approximation schemes for Steiner tree and forest in low-dimensional spaces. / Bartal, Yair; Gottlieb, Lee Ad.
STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. ed. / Samir Khuller; Virginia Vassilevska Williams. Association for Computing Machinery, 2021. p. 1028-1041 (Proceedings of the Annual ACM Symposium on Theory of Computing).

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

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Bartal Y, Gottlieb LA. Near-linear time approximation schemes for Steiner tree and forest in low-dimensional spaces. In Khuller S, Williams VV, editors, STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. Association for Computing Machinery. 2021. p. 1028-1041. (Proceedings of the Annual ACM Symposium on Theory of Computing). doi: 10.1145/3406325.3451063

Near-linear time approximation schemes for Steiner tree and forest in low-dimensional spaces

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Keywords

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