Better Tradeoffs for Exact Distance Oracles in Planar Graphs [chapter]

Pawel Gawrychowski, Shay Mozes, Oren Weimann, Christian Wulff-Nilsen
<span title="">2018</span> <i title="Society for Industrial and Applied Mathematics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ja7dpjgz2nhjlovlil3ij5m7ei" style="color: black;">Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms</a> </i> &nbsp;
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
more &raquo; ... nd query-time. For any S ∈ [n, n 2 ], we show an oracle of size S that answers queries in Õ(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 ∈ [n, n 5/3 ].
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