Metric embedding via shortest path decompositions

Ittai Abraham; Anupam Gupta; Arnold Filtser; Ofer Neiman

doi:10.1145/3188745.3188808

Metric embedding via shortest path decompositions

Ittai Abraham, Anupam Gupta, Arnold Filtser, Ofer Neiman

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

10 Scopus citations

Abstract

We study the problem of embedding weighted graphs of pathwidth k into ℓ_p spaces. Our main result is an O(k^min {1/p^{, 1}/2 ^})-distortion embedding. For p = 1, this is a super-exponential improvement over the best previous bound of Lee and Sidiropoulos. Our distortion bound is asymptotically tight for any fixed p > 1. Our result is obtained via a novel embedding technique that is based on low depth decompositions of a graph via shortest paths. The core new idea is that given a geodesic shortest path P, we can probabilistically embed all points into 2 dimensions with respect to P. For p > 2 our embedding also implies improved distortion on bounded treewidth graphs (O((k log n)¹/^p)). For asymptotically large p, our results also implies improved distortion on graphs excluding a minor.

Original language	English
Title of host publication	STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing
Editors	Monika Henzinger, David Kempe, Ilias Diakonikolas
Publisher	Association for Computing Machinery
Pages	912-919
Number of pages	8
ISBN (Electronic)	9781450355599
DOIs	https://doi.org/10.1145/3188745.3188808
State	Published - 20 Jun 2018
Externally published	Yes
Event	50th Annual ACM Symposium on Theory of Computing, STOC 2018 - Los Angeles, United States Duration: 25 Jun 2018 → 29 Jun 2018

Publication series

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

Conference

Conference	50th Annual ACM Symposium on Theory of Computing, STOC 2018
Country/Territory	United States
City	Los Angeles
Period	25/06/18 → 29/06/18

Bibliographical note

Publisher Copyright:
© 2018 Association for Computing Machinery.

Funding

Arnold Filtser is Partially supported by the Lynn and William Frankel Center for Computer Sciences, ISF grant 1817/17, and by BSF Grant 2015813. Anupam Gupta is supported in part by NSF awards CCF-1536002, CCF-1540541, and CCF-1617790. Ofer Neiman is supported in part by ISF grant 1817/17, and by BSF Grant 2015813.

Funders	Funder number
Barth Syndrome Foundation	2015813
National Stroke Foundation	CCF-1536002, CCF-1617790, CCF-1540541
Israel Science Foundation	1817/17

Keywords

Metric embeddings
Normed spaces
Pathwidth
Shortest path decomposition
Treewidth

Access to Document

10.1145/3188745.3188808

Cite this

Abraham, I., Gupta, A., Filtser, A., & Neiman, O. (2018). Metric embedding via shortest path decompositions. In M. Henzinger, D. Kempe, & I. Diakonikolas (Eds.), STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing (pp. 912-919). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/3188745.3188808

Abraham, Ittai ; Gupta, Anupam ; Filtser, Arnold et al. / Metric embedding via shortest path decompositions. STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing. editor / Monika Henzinger ; David Kempe ; Ilias Diakonikolas. Association for Computing Machinery, 2018. pp. 912-919 (Proceedings of the Annual ACM Symposium on Theory of Computing).

@inproceedings{89ec7563d929438e88384221d8f72457,

title = "Metric embedding via shortest path decompositions",

abstract = "We study the problem of embedding weighted graphs of pathwidth k into ℓp spaces. Our main result is an O(kmin {1/p, 1/2 })-distortion embedding. For p = 1, this is a super-exponential improvement over the best previous bound of Lee and Sidiropoulos. Our distortion bound is asymptotically tight for any fixed p > 1. Our result is obtained via a novel embedding technique that is based on low depth decompositions of a graph via shortest paths. The core new idea is that given a geodesic shortest path P, we can probabilistically embed all points into 2 dimensions with respect to P. For p > 2 our embedding also implies improved distortion on bounded treewidth graphs (O((k log n)1/p)). For asymptotically large p, our results also implies improved distortion on graphs excluding a minor.",

keywords = "Metric embeddings, Normed spaces, Pathwidth, Shortest path decomposition, Treewidth",

author = "Ittai Abraham and Anupam Gupta and Arnold Filtser and Ofer Neiman",

note = "Publisher Copyright: {\textcopyright} 2018 Association for Computing Machinery.; 50th Annual ACM Symposium on Theory of Computing, STOC 2018 ; Conference date: 25-06-2018 Through 29-06-2018",

year = "2018",

month = jun,

day = "20",

doi = "10.1145/3188745.3188808",

language = "אנגלית",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

publisher = "Association for Computing Machinery",

pages = "912--919",

editor = "Monika Henzinger and David Kempe and Ilias Diakonikolas",

booktitle = "STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing",

}

Abraham, I, Gupta, A, Filtser, A & Neiman, O 2018, Metric embedding via shortest path decompositions. in M Henzinger, D Kempe & I Diakonikolas (eds), STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 912-919, 50th Annual ACM Symposium on Theory of Computing, STOC 2018, Los Angeles, United States, 25/06/18. https://doi.org/10.1145/3188745.3188808

Metric embedding via shortest path decompositions. / Abraham, Ittai; Gupta, Anupam; Filtser, Arnold et al.
STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing. ed. / Monika Henzinger; David Kempe; Ilias Diakonikolas. Association for Computing Machinery, 2018. p. 912-919 (Proceedings of the Annual ACM Symposium on Theory of Computing).

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

TY - GEN

T1 - Metric embedding via shortest path decompositions

AU - Abraham, Ittai

AU - Gupta, Anupam

AU - Filtser, Arnold

AU - Neiman, Ofer

PY - 2018/6/20

Y1 - 2018/6/20

N2 - We study the problem of embedding weighted graphs of pathwidth k into ℓp spaces. Our main result is an O(kmin {1/p, 1/2 })-distortion embedding. For p = 1, this is a super-exponential improvement over the best previous bound of Lee and Sidiropoulos. Our distortion bound is asymptotically tight for any fixed p > 1. Our result is obtained via a novel embedding technique that is based on low depth decompositions of a graph via shortest paths. The core new idea is that given a geodesic shortest path P, we can probabilistically embed all points into 2 dimensions with respect to P. For p > 2 our embedding also implies improved distortion on bounded treewidth graphs (O((k log n)1/p)). For asymptotically large p, our results also implies improved distortion on graphs excluding a minor.

AB - We study the problem of embedding weighted graphs of pathwidth k into ℓp spaces. Our main result is an O(kmin {1/p, 1/2 })-distortion embedding. For p = 1, this is a super-exponential improvement over the best previous bound of Lee and Sidiropoulos. Our distortion bound is asymptotically tight for any fixed p > 1. Our result is obtained via a novel embedding technique that is based on low depth decompositions of a graph via shortest paths. The core new idea is that given a geodesic shortest path P, we can probabilistically embed all points into 2 dimensions with respect to P. For p > 2 our embedding also implies improved distortion on bounded treewidth graphs (O((k log n)1/p)). For asymptotically large p, our results also implies improved distortion on graphs excluding a minor.

KW - Metric embeddings

KW - Normed spaces

KW - Pathwidth

KW - Shortest path decomposition

KW - Treewidth

UR - http://www.scopus.com/inward/record.url?scp=85049885675&partnerID=8YFLogxK

U2 - 10.1145/3188745.3188808

DO - 10.1145/3188745.3188808

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85049885675

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 912

EP - 919

BT - STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing

A2 - Henzinger, Monika

A2 - Kempe, David

A2 - Diakonikolas, Ilias

PB - Association for Computing Machinery

T2 - 50th Annual ACM Symposium on Theory of Computing, STOC 2018

Y2 - 25 June 2018 through 29 June 2018

ER -

Abraham I, Gupta A, Filtser A, Neiman O. Metric embedding via shortest path decompositions. In Henzinger M, Kempe D, Diakonikolas I, editors, STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing. Association for Computing Machinery. 2018. p. 912-919. (Proceedings of the Annual ACM Symposium on Theory of Computing). doi: 10.1145/3188745.3188808

Metric embedding via shortest path decompositions

Abstract

Publication series

Conference

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this