Almost optimal distance oracles for planar graphs

Panagiotis Charalampopoulos; Paweł Gawrychowski; Shay Mozes; Oren Weimann

doi:10.1145/3313276.3316316

Almost optimal distance oracles for planar graphs

Panagiotis Charalampopoulos, Paweł Gawrychowski, Shay Mozes, Oren Weimann

Department of Computer Science

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

Abstract

We present new tradeoffs between space and query-time for exact distance oracles in directed weighted planar graphs. These tradeoffs are almost optimal in the sense that they are within polylogarithmic, subpolynomial or arbitrarily small polynomial factors from the naïve linear space, constant query-time lower bound. These tradeoffs include: (i) an oracle with space O(n¹+^ϵ) and query-time Õ(1) for any constant ϵ > 0, (ii) an oracle with space Õ(n) and query-time O(n^ϵ) for any constant ϵ > 0, and (iii) an oracle with space n¹+o(1⁾ and query-time n^o(1⁾.

Original language	English
Title of host publication	STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
Editors	Moses Charikar, Edith Cohen
Publisher	Association for Computing Machinery
Pages	138-151
Number of pages	14
ISBN (Electronic)	9781450367059
DOIs	https://doi.org/10.1145/3313276.3316316
State	Published - 23 Jun 2019
Event	51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States Duration: 23 Jun 2019 → 26 Jun 2019

Publication series

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

Conference

Conference	51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019
Country/Territory	United States
City	Phoenix
Period	23/06/19 → 26/06/19

Bibliographical note

Publisher Copyright:
© 2019 Association for Computing Machinery.

Keywords

Distance oracles
Planar graphs
Shortest paths
Voronoi diagrams

ASJC Scopus subject areas

Software

Access to Document

10.1145/3313276.3316316

Cite this

Charalampopoulos, P., Gawrychowski, P., Mozes, S., & Weimann, O. (2019). Almost optimal distance oracles for planar graphs. In M. Charikar, & E. Cohen (Eds.), STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (pp. 138-151). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/3313276.3316316

Charalampopoulos, Panagiotis ; Gawrychowski, Paweł ; Mozes, Shay et al. / Almost optimal distance oracles for planar graphs. STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. editor / Moses Charikar ; Edith Cohen. Association for Computing Machinery, 2019. pp. 138-151 (Proceedings of the Annual ACM Symposium on Theory of Computing).

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title = "Almost optimal distance oracles for planar graphs",

abstract = "We present new tradeoffs between space and query-time for exact distance oracles in directed weighted planar graphs. These tradeoffs are almost optimal in the sense that they are within polylogarithmic, subpolynomial or arbitrarily small polynomial factors from the na{\"i}ve linear space, constant query-time lower bound. These tradeoffs include: (i) an oracle with space O(n1+ϵ) and query-time {\~O}(1) for any constant ϵ > 0, (ii) an oracle with space {\~O}(n) and query-time O(nϵ) for any constant ϵ > 0, and (iii) an oracle with space n1+o(1) and query-time no(1).",

keywords = "Distance oracles, Planar graphs, Shortest paths, Voronoi diagrams",

author = "Panagiotis Charalampopoulos and Pawe{\l} Gawrychowski and Shay Mozes and Oren Weimann",

note = "Publisher Copyright: {\textcopyright} 2019 Association for Computing Machinery.; 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 ; Conference date: 23-06-2019 Through 26-06-2019",

year = "2019",

month = jun,

day = "23",

doi = "10.1145/3313276.3316316",

language = "English",

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

publisher = "Association for Computing Machinery",

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Charalampopoulos, P, Gawrychowski, P, Mozes, S & Weimann, O 2019, Almost optimal distance oracles for planar graphs. in M Charikar & E Cohen (eds), STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 138-151, 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019, Phoenix, United States, 23/06/19. https://doi.org/10.1145/3313276.3316316

Almost optimal distance oracles for planar graphs. / Charalampopoulos, Panagiotis; Gawrychowski, Paweł; Mozes, Shay et al.
STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. ed. / Moses Charikar; Edith Cohen. Association for Computing Machinery, 2019. p. 138-151 (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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AU - Charalampopoulos, Panagiotis

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N2 - We present new tradeoffs between space and query-time for exact distance oracles in directed weighted planar graphs. These tradeoffs are almost optimal in the sense that they are within polylogarithmic, subpolynomial or arbitrarily small polynomial factors from the naïve linear space, constant query-time lower bound. These tradeoffs include: (i) an oracle with space O(n1+ϵ) and query-time Õ(1) for any constant ϵ > 0, (ii) an oracle with space Õ(n) and query-time O(nϵ) for any constant ϵ > 0, and (iii) an oracle with space n1+o(1) and query-time no(1).

AB - We present new tradeoffs between space and query-time for exact distance oracles in directed weighted planar graphs. These tradeoffs are almost optimal in the sense that they are within polylogarithmic, subpolynomial or arbitrarily small polynomial factors from the naïve linear space, constant query-time lower bound. These tradeoffs include: (i) an oracle with space O(n1+ϵ) and query-time Õ(1) for any constant ϵ > 0, (ii) an oracle with space Õ(n) and query-time O(nϵ) for any constant ϵ > 0, and (iii) an oracle with space n1+o(1) and query-time no(1).

KW - Distance oracles

KW - Planar graphs

KW - Shortest paths

KW - Voronoi diagrams

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Charalampopoulos P, Gawrychowski P, Mozes S, Weimann O. Almost optimal distance oracles for planar graphs. In Charikar M, Cohen E, editors, STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. Association for Computing Machinery. 2019. p. 138-151. (Proceedings of the Annual ACM Symposium on Theory of Computing). doi: 10.1145/3313276.3316316

Almost optimal distance oracles for planar graphs

Abstract

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Bibliographical note

Keywords

ASJC Scopus subject areas

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