We present a simple wavefront-like approach for computing multiplicatively weighted Voronoi diagrams of points and straight-line segments in the Euclidean plane. If the input sites may be assumed to be randomly weighted points then the use of a so-called overlay arrangement [Har-Peled&Raichel, Discrete Comput. Geom. 53:547-568, 2015] allows to achieve an expected runtime complexity of $O(n\log^4 n)$, while still maintaining the simplicity of our approach. We implemented the full algorithm for weighted points as input sites, based on CGAL. The results of an experimental evaluation of our implementation suggest $O(n\log^2 n)$ as a practical bound on the runtime. Our algorithm can be extended to handle also additive weights in addition to multiplicative weights, and it yields a truly simple $O(n\log n)$ solution for solving the one-dimensional version of this problem.

中文翻译：

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一种计算乘法加权 Voronoi 图的高效实用算法和实现

我们提出了一种简单的类似波前的方法，用于计算欧几里得平面中点和直线段的乘法加权 Voronoi 图。如果可以假设输入站点是随机加权的点，则使用所谓的重叠排列 [Har-Peled & Raichel, Discrete Comput. 杰姆。53:547-568, 2015] 允许实现 $O(n\log^4 n)$ 的预期运行时复杂度，同时仍然保持我们方法的简单性。我们基于 CGAL 实现了将加权点作为输入站点的完整算法。我们实现的实验评估结果表明 $O(n\log^2 n)$ 作为运行时的实际界限。我们的算法可以扩展到除了乘法权重之外还可以处理加法权重，