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arXiv 2012.069782020-12-13cs.CG

Largest similar copies of convex polygons amidst polygonal obstacles

Taekang Eom, Seungjun Lee, Hee-Kap Ahn

英文摘要：

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 $O(k^2n^2λ_4(k)\log{n})$. 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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