Truly Subquadratic Exact Distance Oracles with Constant Query Time for Planar Graphs
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Given an undirected, unweighted planar graph G with n vertices, we present a truly subquadratic size distance oracle for reporting exact shortest-path distances between any pair of vertices of G in constant time. For any ε > 0, our distance oracle takes up O(n^5/3+ε) space and is capable of answering shortest-path distance queries exactly for any pair of vertices of G in worst-case time O(log (1/ε)). Previously no truly sub-quadratic size distance oracles with constant query time for answering exact all-pairs shortest paths distance queries existed.
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