Efficient nearest-neighbor query and clustering of planar curves

Boris Aronov, Omrit Filtser, Michael Horton, Matthew J. Katz, Khadijeh Sheikhan

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    We study two fundamental problems dealing with curves in the plane, namely, the nearest-neighbor problem and the center problem. Let C be a set of n polygonal curves, each of size m. In the nearest-neighbor problem, the goal is to construct a compact data structure over C, such that, given a query curve Q, one can efficiently find the curve in C closest to Q. In the center problem, the goal is to find a curve Q, such that the maximum distance between Q and the curves in C is minimized. We use the well-known discrete Fréchet distance function, both under L and under L2, to measure the distance between two curves. For the nearest-neighbor problem, despite discouraging previous results, we identify two important cases for which it is possible to obtain practical bounds, even when m and n are large. In these cases, either Q is a line segment or C consists of line segments, and the bounds on the size of the data structure and query time are nearly linear in the size of the input and query curve, respectively. The returned answer is either exact under L, or approximated to within a factor of 1 + ε under L2. We also consider the variants in which the location of the input curves is only fixed up to translation, and obtain similar bounds, under L. As for the center problem, we study the case where the center is a line segment, i.e., we seek the line segment that represents the given set as well as possible. We present near-linear time exact algorithms under L, even when the location of the input curves is only fixed up to translation. Under L2, we present a roughly O(n2m3) -time exact algorithm.

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings
    EditorsZachary Friggstad, Mohammad R. Salavatipour, Jörg-Rüdiger Sack
    PublisherSpringer Verlag
    Pages28-42
    Number of pages15
    ISBN (Print)9783030247652
    DOIs
    StatePublished - 2019
    Event16th International Symposium on Algorithms and Data Structures, WADS 2019 - Edmonton, Canada
    Duration: Aug 5 2019Aug 7 2019

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume11646 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Conference

    Conference16th International Symposium on Algorithms and Data Structures, WADS 2019
    CountryCanada
    CityEdmonton
    Period8/5/198/7/19

    Keywords

    • (Approximation) algorithms
    • Clustering
    • Data structures
    • Fréchet distance
    • Nearest-neighbor queries
    • Polygonal curves

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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  • Cite this

    Aronov, B., Filtser, O., Horton, M., Katz, M. J., & Sheikhan, K. (2019). Efficient nearest-neighbor query and clustering of planar curves. In Z. Friggstad, M. R. Salavatipour, & J-R. Sack (Eds.), Algorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings (pp. 28-42). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11646 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-24766-9_3