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 ∈ [n, n 2 ], we show an oracle of size S that answers queries inÕ(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 ].
The currently best known tradeoff is an oracle of sizeÕ(n 3/2 /q), that answers queries in timeÕ(q) for any q ∈ [1, n 1/2 ] REF .
Better Tradeoffs for Exact Distance Oracles in Planar Graphs
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ArXiv
Mathematics Computer Science