Approximation algorithms for computing partitions with minimum stabbing number of rectilinear and simple polygons

Mohammad Ali Abam, Boris Aronov, Mark De Berg, Amirali Khosravi

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

    Abstract

    Let P be a rectilinear simple polygon. The stabbing number of a partition of P into rectangles is the maximum number of rectangles stabbed by any axis-parallel line segment inside P. We present a 3-approximation algorithm for the problem of finding a partition with minimum stabbing number. It is based on an algorithm that finds an optimal partition for histograms. We also study Steiner triangulations of a simple (nonrectilinear) polygon P. Here the stabbing number is defined as the maximum number of triangles that can be stabbed by any line segment inside P. We give an O(1)-approximation algorithm for the problem of computing a Steiner triangulation with minimum stabbing number.

    Original languageEnglish (US)
    Title of host publicationProceedings of the 27th Annual Symposium on Computational Geometry, SCG'11
    Pages407-416
    Number of pages10
    DOIs
    StatePublished - 2011
    Event27th Annual ACM Symposium on Computational Geometry, SCG'11 - Paris, France
    Duration: Jun 13 2011Jun 15 2011

    Other

    Other27th Annual ACM Symposium on Computational Geometry, SCG'11
    CountryFrance
    CityParis
    Period6/13/116/15/11

    Fingerprint

    Simple Polygon
    Approximation algorithms
    Triangulation
    Approximation Algorithms
    Partition
    Computing
    Line segment
    Rectangle
    Optimal Partition
    Histogram
    Triangle

    Keywords

    • Approximation algorithms
    • Computational geometry
    • Polygons
    • Rectangular decompositions
    • Stabbing number
    • Steiner triangulations

    ASJC Scopus subject areas

    • Computational Mathematics
    • Geometry and Topology
    • Theoretical Computer Science

    Cite this

    Abam, M. A., Aronov, B., De Berg, M., & Khosravi, A. (2011). Approximation algorithms for computing partitions with minimum stabbing number of rectilinear and simple polygons. In Proceedings of the 27th Annual Symposium on Computational Geometry, SCG'11 (pp. 407-416) https://doi.org/10.1145/1998196.1998263

    Approximation algorithms for computing partitions with minimum stabbing number of rectilinear and simple polygons. / Abam, Mohammad Ali; Aronov, Boris; De Berg, Mark; Khosravi, Amirali.

    Proceedings of the 27th Annual Symposium on Computational Geometry, SCG'11. 2011. p. 407-416.

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

    Abam, MA, Aronov, B, De Berg, M & Khosravi, A 2011, Approximation algorithms for computing partitions with minimum stabbing number of rectilinear and simple polygons. in Proceedings of the 27th Annual Symposium on Computational Geometry, SCG'11. pp. 407-416, 27th Annual ACM Symposium on Computational Geometry, SCG'11, Paris, France, 6/13/11. https://doi.org/10.1145/1998196.1998263
    Abam MA, Aronov B, De Berg M, Khosravi A. Approximation algorithms for computing partitions with minimum stabbing number of rectilinear and simple polygons. In Proceedings of the 27th Annual Symposium on Computational Geometry, SCG'11. 2011. p. 407-416 https://doi.org/10.1145/1998196.1998263
    Abam, Mohammad Ali ; Aronov, Boris ; De Berg, Mark ; Khosravi, Amirali. / Approximation algorithms for computing partitions with minimum stabbing number of rectilinear and simple polygons. Proceedings of the 27th Annual Symposium on Computational Geometry, SCG'11. 2011. pp. 407-416
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