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].
|Title of host publication||29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018|
|Publisher||Association for Computing Machinery|
|Number of pages||15|
|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
|Name||Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms|
|Conference||29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018|
|Period||7/01/18 → 10/01/18|
Bibliographical noteFunding Information:
‡Universityof Haifa, DepartmentofComputerScience, firstname.lastname@example.org. Partially supported by the Israel Science Foundationgrants 794/13and592/17.
†IDCHerzliya, EfiAraziSchoolofComputerScience, email@example.com. Partially supported by the Israel Science Foun-dationgrants 794/13and592/17.
© Copyright 2018 by SIAM.
ASJC Scopus subject areas
- Mathematics (all)