We present a truly subquadratic size distance oracle for reporting, in constant time, the exact shortest-path distance between any pair of vertices of an undirected, unweighted planar graph G. For any ε > 0, our distance oracle requires 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 shortest paths distance queries existed.
@InProceedings{fredslundhansen_et_al:LIPIcs.ISAAC.2021.25, author = {Fredslund-Hansen, Viktor and Mozes, Shay and Wulff-Nilsen, Christian}, title = {{Truly Subquadratic Exact Distance Oracles with Constant Query Time for Planar Graphs}}, booktitle = {32nd International Symposium on Algorithms and Computation (ISAAC 2021)}, pages = {25:1--25:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-214-3}, ISSN = {1868-8969}, year = {2021}, volume = {212}, editor = {Ahn, Hee-Kap and Sadakane, Kunihiko}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.25}, URN = {urn:nbn:de:0030-drops-154586}, doi = {10.4230/LIPIcs.ISAAC.2021.25}, annote = {Keywords: distance oracle, planar graph, shortest paths, subquadratic} }
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