非交叉簇的Hausdorff沃罗诺伊图的随机增量构造
Randomized incremental construction of the Hausdorff Voronoi diagram of non-crossing clusters
摘要：
在平面上一组点簇的Hausdorff沃罗诺伊图中，点t和簇P之间的距离是t和P中的点之间的最大欧氏距离。该图在VLSI设计中有直接的应用。我们考虑所谓的“非交叉”集群。m个这样的簇的Hausdorff图的复杂度与所有簇的凸包中的点的总数n成线性关系。我们提出了随机增量结构计算效率的图，大大提高了以前的结果。我们的最佳复杂度算法运行在预期时间O（（n + m（log log（n））^2）log^2（n））和最坏情况空间O（n）。我们还给出了一个更实用的算法，其预期运行时间为O（（n + mlog（n））log^2（n）），预期空间复杂度为O（n）.为了实现这些界限，我们增加了随机增量范例建设的沃罗诺伊图的能力，有效地处理非标准的特性，广义沃罗诺伊图，如网站的非恒定复杂性，网站，不封闭在他们的沃罗诺伊地区，空沃罗诺伊地区。
英文摘要：
In the Hausdorff Voronoi diagram of a set of clusters of points in the plane, the distance between a point t and a cluster P is the maximum Euclidean distance between t and a point in P. This diagram has direct applications in VLSI design. We consider so-called "non-crossing" clusters. The complexity of the Hausdorff diagram of m such clusters is linear in the total number n of points in the convex hulls of all clusters. We present randomized incremental constructions for computing efficiently the diagram, improving considerably previous results. Our best complexity algorithm runs in expected time O((n + m(log log(n))^2)log^2(n)) and worst-case space O(n). We also provide a more practical algorithm whose expected running time is O((n + m log(n))log^2(n)) and expected space complexity is O(n). To achieve these bounds, we augment the randomized incremental paradigm for the construction of Voronoi diagrams with the ability to efficiently handle non-standard characteristics of generalized Voronoi diagrams, such as sites of non-constant complexity, sites that are not enclosed in their Voronoi regions, and empty Voronoi regions.
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