Searching edges in the overlap of two plane graphs

John Iacono, Elena Khramtcova, Stefan Langerman

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

    Abstract

    Consider a pair of plane straight-line graphs whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n log n)-time O(n)-space technique to preprocess such a pair of graphs, that enables efficient searches among the red-blue intersections along edges of one of the graphs. Our technique has a number of applications to geometric problems. This includes: (1) a solution to the batched red-blue search problem [Dehne et al. 2006] in O(n log n) queries to the oracle; (2) an algorithm to compute the maximum vertical distance between a pair of 3D polyhedral terrains, one of which is convex, in O(n log n) time, where n is the total complexity of both terrains; (3) an algorithm to construct the Hausdorff Voronoi diagram of a family of point clusters in the plane in O((n+m) log3n) time and O(n + m) space, where n is the total number of points in all clusters and m is the number of crossings between all clusters; (4) an algorithm to construct the farthest-color Voronoi diagram of the corners of n disjoint axis-aligned rectangles in O(n log2n) time; (5) an algorithm to solve the stabbing circle problem for n parallel line segments in the plane in optimal O(n log n) time. All these results are new or improve on the best known algorithms.

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings
    PublisherSpringer Verlag
    Pages473-484
    Number of pages12
    Volume10389 LNCS
    ISBN (Print)9783319621265
    DOIs
    StatePublished - 2017
    Event15th International Symposium on Algorithms and Data Structures, WADS 2017 - St. John’s, Canada
    Duration: Jul 31 2017Aug 2 2017

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume10389 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other15th International Symposium on Algorithms and Data Structures, WADS 2017
    CountryCanada
    CitySt. John’s
    Period7/31/178/2/17

    Fingerprint

    Plane Graph
    Overlap
    Voronoi Diagram
    Graph in graph theory
    Polyhedral Terrains
    Line Graph
    Search Problems
    Line segment
    Straight Line
    Rectangle
    Disjoint
    Circle
    Intersection
    Vertical
    Query
    Color

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Iacono, J., Khramtcova, E., & Langerman, S. (2017). Searching edges in the overlap of two plane graphs. In Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings (Vol. 10389 LNCS, pp. 473-484). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10389 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-62127-2_40

    Searching edges in the overlap of two plane graphs. / Iacono, John; Khramtcova, Elena; Langerman, Stefan.

    Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings. Vol. 10389 LNCS Springer Verlag, 2017. p. 473-484 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10389 LNCS).

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

    Iacono, J, Khramtcova, E & Langerman, S 2017, Searching edges in the overlap of two plane graphs. in Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings. vol. 10389 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10389 LNCS, Springer Verlag, pp. 473-484, 15th International Symposium on Algorithms and Data Structures, WADS 2017, St. John’s, Canada, 7/31/17. https://doi.org/10.1007/978-3-319-62127-2_40
    Iacono J, Khramtcova E, Langerman S. Searching edges in the overlap of two plane graphs. In Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings. Vol. 10389 LNCS. Springer Verlag. 2017. p. 473-484. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-62127-2_40
    Iacono, John ; Khramtcova, Elena ; Langerman, Stefan. / Searching edges in the overlap of two plane graphs. Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings. Vol. 10389 LNCS Springer Verlag, 2017. pp. 473-484 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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