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Computing Skeletons for Rectilinearly Convex Obstacles in the Rectilinear Plane

Author

Listed:
  • Marcus Volz

    (The University of Melbourne)

  • Marcus Brazil

    (The University of Melbourne)

  • Charl Ras

    (The University of Melbourne)

  • Doreen Thomas

    (The University of Melbourne)

Abstract

We introduce the concept of an obstacle skeleton, which is a set of line segments inside a polygonal obstacle $$\omega $$ ω that can be used in place of $$\omega $$ ω when performing intersection tests for obstacle-avoiding network problems in the plane. A skeleton can have significantly fewer line segments compared to the number of line segments in the boundary of the original obstacle, and therefore performing intersection tests on a skeleton (rather than the original obstacle) can significantly reduce the CPU time required by algorithms for computing solutions to obstacle-avoidance problems. A minimum skeleton is a skeleton with the smallest possible number of line segments. We provide an exact $$O(n^2)$$ O ( n 2 ) algorithm for computing minimum skeletons for rectilinear obstacles in the rectilinear plane that are rectilinearly convex.

Suggested Citation

  • Marcus Volz & Marcus Brazil & Charl Ras & Doreen Thomas, 2020. "Computing Skeletons for Rectilinearly Convex Obstacles in the Rectilinear Plane," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 102-133, July.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:1:d:10.1007_s10957-020-01690-1
    DOI: 10.1007/s10957-020-01690-1
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    Cited by:

    1. Nicolau Andrés-Thió & Marcus Brazil & Charl Ras & Doreen Thomas & Marcus Volz, 2022. "An exact algorithm for constructing minimum Euclidean skeletons of polygons," Journal of Global Optimization, Springer, vol. 83(1), pages 137-162, May.

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