Proximate point searching

Erik D. Demaine, John Iacono, Stefan Langerman

    Research output: Contribution to journalArticlepeer-review


    In the 2D point searching problem, the goal is to preprocess n points P={p 1,⋯,p n} in the plane so that, for an online sequence of query points q 1,⋯,q m, it can quickly be determined which (if any) of the elements of P are equal to each query point q i. This problem can be solved in O(logn) time by mapping the problem to one dimension. We present a data structure that is optimized for answering queries quickly when they are geometrically close to the previous successful query. Specifically, our data structure executes queries in time O(logd(q i-1,q i)), where d is some distance function between two points, and uses O(nlogn) space. Our structure works with a variety of distance functions. In contrast, it is proved that, for some of the most intuitive distance functions d, it is impossible to obtain an O(logd(q i-1, q i)) runtime, or any bound that is o(logn).

    Original languageEnglish (US)
    Pages (from-to)29-40
    Number of pages12
    JournalComputational Geometry: Theory and Applications
    Issue number1
    StatePublished - May 2004


    • Distance functions
    • Dynamic finger property
    • Point location

    ASJC Scopus subject areas

    • Computer Science Applications
    • Geometry and Topology
    • Control and Optimization
    • Computational Theory and Mathematics
    • Computational Mathematics


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