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

Paweł Gawrychowski, Shay Mozes, Oren Weimann, Christian Wulff-Nilsen
2017 arXiv   pre-print
We present an O(n^1.5)-space distance oracle for directed planar graphs that answers distance queries in O( 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( 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
more » ... -time. For any S∈ [n,n^2], we show an oracle of size S that answers queries in Õ({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].
arXiv:1708.01386v1 fatcat:226uixbxvjd3zeofowwtraj5au