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    Almost optimal exact distance oracles for planar graphs

    Charalampopoulos, Panagiotis and Gawrychowski, P. and Long, Y. and Mozes, S. and Pettie, S. and Weimann, O. and Wulff-Nilsen, C. (2023) Almost optimal exact distance oracles for planar graphs. Journal of the ACM 70 (2), pp. 1-50. ISSN 0004-5411.

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    We consider the problem of preprocessing a weighted directed planar graph in order to quickly answer exact distance queries. The main tension in this problem is between space S and query time Q, and since the mid-1990s all results had polynomial time-space tradeoffs, e.g., Q = ~ Θ(n/√ S) or Q = ~Θ(n5/2/S3/2). In this article we show that there is no polynomial tradeoff between time and space and that it is possible to simultaneously achieve almost optimal space n1+o(1) and almost optimal query time no(1). More precisely, we achieve the following space-time tradeoffs: n1+o(1) space and log2+o(1) n query time, n log2+o(1) n space and no(1) query time, n4/3+o(1) space and log1+o(1) n query time. We reduce a distance query to a variety of point location problems in additively weighted Voronoi diagrams and develop new algorithms for the point location problem itself using several partially persistent dynamic tree data structures.


    Item Type: Article
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Panagiotis Charalampopoulos
    Date Deposited: 05 Apr 2023 14:39
    Last Modified: 09 Aug 2023 12:54


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