Better tradeoffs for exact distance oracles in planar graphs

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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 languageEnglish
Title of host publicationProceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
EditorsA. Czumaj
PublisherSociety for Industrial and Applied Mathematics
Publication date2018
Pages515-529
ISBN (Electronic)9781611975031
DOIs
Publication statusPublished - 2018
Event29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States
Duration: 7 Jan 201810 Jan 2018

Conference

Conference29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
LandUnited States
ByNew Orleans
Periode07/01/201810/01/2018
SponsorACM Special Interest Group on Algorithms and Computation Theory (SIGACT), SIAM Activity Group on Discrete Mathematics

ID: 204040383