Geometric Pattern Matching Reduces to k -SUM

Boris Aronov, Jean Cardinal

    Research output: Contribution to journalArticlepeer-review


    We prove that some exact geometric pattern matching problems reduce in linear time to k-SUM when the pattern has a fixed size k. This holds in the real RAM model for searching for a similar copy of a set of k≥ 3 points within a set of n points in the plane, and for searching for an affine image of a set of k≥ d+ 2 points within a set of n points in d-space. As corollaries, we obtain improved real RAM algorithms and decision trees for the two problems. In particular, they can be solved by algebraic decision trees of near-linear height.

    Original languageEnglish (US)
    Pages (from-to)850-859
    Number of pages10
    JournalDiscrete and Computational Geometry
    Issue number3
    StatePublished - Oct 2022


    • 3-SUM
    • Geometric pattern matching
    • k-SUM

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Discrete Mathematics and Combinatorics
    • Computational Theory and Mathematics


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