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arXiv · 2012.06978

Largest similar copies of convex polygons amidst polygonal obstacles

Taekang Eom·Seungjun Lee·Hee-Kap Ahn
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Abstract

Given a convex polygon $P$ with $k$ vertices and a polygonal domain $Q$ consisting of polygonal obstacles with total size $n$ in the plane, we study the optimization problem of finding a largest similar copy of $P$ that can be placed in $Q$ without intersecting the obstacles. We improve the time complexity for solving the problem to $O(k^2n^2\lambda_4(k)\log{n})$. This is progress of improving the previously best known results by Chew and Kedem [SoCG89, CGTA93] and Sharir and Toledo [SoCG91, CGTA94] on the problem in more than 25 years.

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Taekang Eom, Seungjun Lee, Hee-Kap Ahn. 2020-12-13. Largest similar copies of convex polygons amidst polygonal obstacles. https://arxiv.org/abs/2012.06978

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