Computing Skeletons for Rectilinearly Convex Obstacles in the Rectilinear Plane

Marcus Volz (), Marcus Brazil, Charl Ras and Doreen Thomas
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Marcus Volz: The University of Melbourne
Marcus Brazil: The University of Melbourne
Charl Ras: The University of Melbourne
Doreen Thomas: The University of Melbourne

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 1, No 6, 102-133

Abstract: 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.

Keywords: Skeletons; Obstacle avoidance; Rectilinear; Steiner trees; 90B10; 52B05; 68U05 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-020-01690-1

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