Better tradeoffs for exact distance oracles in planar graphs

Pawel Gawrychowski; Shay Mozes; Oren Weimann; Christian Wulff-Nilsen

doi:https://doi.org/10.1137/1.9781611975031.34

Better tradeoffs for exact distance oracles in planar graphs

Pawel Gawrychowski, Shay Mozes, Oren Weimann, Christian Wulff-Nilsen

Department of Computer Science

University of Haifa

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

Abstract

We present an O(n1:5)-space distance oracle for directed planar graphs that answers distance queries in O(log n) time. Our oracle both significantly simplifies and significantly improves the recent oracle of Cohen-Addad, Dahlgaard and Wulff-Nilsen [FOCS 2017], which uses O(n5=3)-space and answers queries in O(log n) time. We achieve this by designing an elegant and efficient point location data structure for Voronoi diagrams on planar graphs. We further show a smooth tradeoff between space and query-time. For any S 2 [n; n2], we show an oracle of size S that answers queries in ~O (maxf1; n1:5=Sg) time. This new tradeoff is currently the best (up to polylogarithmic factors) for the entire range of S and improves by polynomial factors over all previously known tradeoffs for the range S 2 [n; n5=3].

Original language	American English
Title of host publication	29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Editors	Artur Czumaj
Publisher	Association for Computing Machinery
Pages	515-529
Number of pages	15
ISBN (Electronic)	9781611975031
DOIs	https://doi.org/10.1137/1.9781611975031.34
State	Published - 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

All Science Journal Classification (ASJC) codes

Software
General Mathematics

Access to Document

https://doi.org/10.1137/1.9781611975031.34

Cite this

Gawrychowski, P., Mozes, S., Weimann, O., & Wulff-Nilsen, C. (2018). Better tradeoffs for exact distance oracles in planar graphs. In A. Czumaj (Ed.), 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 (pp. 515-529). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery. https://doi.org/10.1137/1.9781611975031.34

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title = "Better tradeoffs for exact distance oracles in planar graphs",

abstract = "We present an O(n1:5)-space distance oracle for directed planar graphs that answers distance queries in O(log n) time. Our oracle both significantly simplifies and significantly improves the recent oracle of Cohen-Addad, Dahlgaard and Wulff-Nilsen [FOCS 2017], which uses O(n5=3)-space and answers queries in O(log n) time. We achieve this by designing an elegant and efficient point location data structure for Voronoi diagrams on planar graphs. We further show a smooth tradeoff between space and query-time. For any S 2 [n; n2], we show an oracle of size S that answers queries in ~O (maxf1; n1:5=Sg) time. This new tradeoff is currently the best (up to polylogarithmic factors) for the entire range of S and improves by polynomial factors over all previously known tradeoffs for the range S 2 [n; n5=3].",

author = "Pawel Gawrychowski and Shay Mozes and Oren Weimann and Christian Wulff-Nilsen",

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Gawrychowski, P, Mozes, S, Weimann, O & Wulff-Nilsen, C 2018, Better tradeoffs for exact distance oracles in planar graphs. 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. 515-529, 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, United States, 7/01/18. https://doi.org/10.1137/1.9781611975031.34

Better tradeoffs for exact distance oracles in planar graphs. / Gawrychowski, Pawel; Mozes, Shay; Weimann, Oren et al.
29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. ed. / Artur Czumaj. Association for Computing Machinery, 2018. p. 515-529 (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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Gawrychowski P, Mozes S, Weimann O, Wulff-Nilsen C. Better tradeoffs for exact distance oracles in planar graphs. In Czumaj A, editor, 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Association for Computing Machinery. 2018. p. 515-529. (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). doi: https://doi.org/10.1137/1.9781611975031.34

Better tradeoffs for exact distance oracles in planar graphs

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