Better Tradeoffs for Exact Distance Oracles in Planar Graphs
(1708.01386)Abstract
We present an $O(n{1.5})$-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 $O(n{5/3})$-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 $S\in [n,n2]$, we show an oracle of size $S$ that answers queries in $\tilde O(\max{1,n{1.5}/S})$ 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 the previously known tradeoffs for the range $S \in [n,n{5/3}]$.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.