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 | English |
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| Title of host publication | Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms |
| Editors | A. Czumaj |
| Publisher | Society for Industrial and Applied Mathematics |
| Publication date | 2018 |
| Pages | 515-529 |
| ISBN (Electronic) | 9781611975031 |
| DOIs | |
| Publication status | Published - 2018 |
| Event | 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States Duration: 7 Jan 2018 → 10 Jan 2018 |
Conference
| Conference | 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 |
|---|---|
| Country/Territory | United States |
| City | New Orleans |
| Period | 07/01/2018 → 10/01/2018 |
| Sponsor | ACM Special Interest Group on Algorithms and Computation Theory (SIGACT), SIAM Activity Group on Discrete Mathematics |