Two-point Euclidean shortest path queries in the plane

Yi-Jen Chiang, Joseph S B Mitchell

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

    Abstract

    We consider the two-point query version of the fundamental geometric shortest path problem: Given a set h of polygonal obstacles in the plane, having a total of n vertices, build a data structure such that for any two query points s and t we can efficiently determine the length, d(s,t), of an Euclidean shortest obstacle-avoiding path, π(s, t), from s to t. Additionally, our data structure should allow one to report the path π(s, t), in time proportional to its (combinatorial) size. We present various methods for solving this two-point query problem, including algorithms with o(n), O(log n+h), O(h log n), O(log2 n) or optimal O(log n) query times, using polynomial-space data structures, with various tradeoffs between space and query time. While several results have been known for approximate two-point Euclidean shortest path queries, it has been a well-publicized open problem to obtain sublinear query time for the exact version of the problem. Our methods also yield data structures for two-point shortest path queries on nonconvex polyhedral surfaces.

    Original languageEnglish (US)
    Title of host publicationProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
    Editors Anon
    PublisherSIAM
    Pages215-224
    Number of pages10
    StatePublished - 1999
    EventProceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms - Baltimore, MD, USA
    Duration: Jan 17 1999Jan 19 1999

    Other

    OtherProceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms
    CityBaltimore, MD, USA
    Period1/17/991/19/99

    Fingerprint

    Shortest path
    Data structures
    Euclidean
    Query
    Data Structures
    Polynomials
    Path
    Shortest Path Problem
    Open Problems
    Polynomial time
    Trade-offs
    Directly proportional

    ASJC Scopus subject areas

    • Chemical Health and Safety
    • Software
    • Safety, Risk, Reliability and Quality
    • Discrete Mathematics and Combinatorics

    Cite this

    Chiang, Y-J., & Mitchell, J. S. B. (1999). Two-point Euclidean shortest path queries in the plane. In Anon (Ed.), Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 215-224). SIAM.

    Two-point Euclidean shortest path queries in the plane. / Chiang, Yi-Jen; Mitchell, Joseph S B.

    Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. ed. / Anon. SIAM, 1999. p. 215-224.

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

    Chiang, Y-J & Mitchell, JSB 1999, Two-point Euclidean shortest path queries in the plane. in Anon (ed.), Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM, pp. 215-224, Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, USA, 1/17/99.
    Chiang Y-J, Mitchell JSB. Two-point Euclidean shortest path queries in the plane. In Anon, editor, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM. 1999. p. 215-224
    Chiang, Yi-Jen ; Mitchell, Joseph S B. / Two-point Euclidean shortest path queries in the plane. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. editor / Anon. SIAM, 1999. pp. 215-224
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