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تسجيل مستخدم جديدThe Geodesic Farthest-point Voronoi Diagram in a Simple Polygon
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Given a set of point sites in a simple polygon, the geodesic farthest-point Voronoi diagram partitions the polygon into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the geodesic metric. We present an $O(nloglog n+mlog m)$- time algorithm to compute the geodesic farthest-point Voronoi diagram of $m$ point sites in a simple $n$-gon. This improves the previously best known algorithm by Aronov et al. [Discrete Comput. Geom. 9(3):217-255, 1993]. In the case that all point sites are on the boundary of the simple polygon, we can compute the geodesic farthest-point Voronoi diagram in $O((n + m) log log n)$ time.
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Let $P$ be a simple polygon with $n$ vertices. For any two points in $P$, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in $P$. Given a set $S$ of $m$ sites being a subset of the ve
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