The $L_\infty$ Hausdorff Voronoi Diagram Revisited

2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering Pub Date : 2011-06-28 DOI:10.1109/ISVD.2011.17

Evanthia Papadopoulou, Jinhui Xu

引用次数: 4

Abstract

We revisit the L-infinity Hausdorff Voronoi diagram of clusters of points, equivalently, the L-infinity Hausdorff Voronoi diagram of rectangles, and present a plane sweep algorithm for its construction that generalizes and improves upon previous results. We show that the structural complexity of the L-infinity Hausdorff Voronoi diagram is Theta(n+m), where n is the number of given clusters and m is the number of essential pairs of crossing clusters. The algorithm runs in O((n+M)\log n) time and O(n+M) space where M is the number of potentially essential crossings; m, M are O(n^2), m = M, but m = M, in the worst case. In practice m;M

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重新访问$L_\infty$ Hausdorff Voronoi图

我们重新审视了点簇的l -∞Hausdorff Voronoi图，相当于矩形的l -∞Hausdorff Voronoi图，并提出了一个平面扫描算法来构建它，该算法在之前的结果基础上进行了推广和改进。我们证明了l -∞Hausdorff Voronoi图的结构复杂性是Theta(n+m)，其中n是给定簇的数量，m是交叉簇的基本对的数量。该算法在O((n+M)\log n)时间和O(n+M)空间内运行，其中M是潜在必要交叉的数量;m m是O(n²)m = m，最坏情况下m = m。在实践中

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering

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