BIROn - Birkbeck Institutional Research Online

    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.

    [img]
    Preview
    Text
    main.pdf - Author's Accepted Manuscript

    Download (7MB) | Preview

    Abstract

    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.

    Metadata

    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
    URI: https://eprints.bbk.ac.uk/id/eprint/50932

    Statistics

    Activity Overview
    6 month trend
    102Downloads
    6 month trend
    150Hits

    Additional statistics are available via IRStats2.

    Archive Staff Only (login required)

    Edit/View Item Edit/View Item