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An improved construction for spanners of disks
Computational Geometry ( IF 0.4 ) Pub Date : 2020-07-01 , DOI: 10.1016/j.comgeo.2020.101682 Michiel Smid
中文翻译:
磁盘扳手的改进结构
更新日期:2020-07-01
Computational Geometry ( IF 0.4 ) Pub Date : 2020-07-01 , DOI: 10.1016/j.comgeo.2020.101682 Michiel Smid
Let be a set of n pairwise disjoint disks in the plane. Consider the metric space in which the distance between any two disks D and in is the length of the shortest line segment that connects D and . For any real number , we show how to obtain a -spanner for this metric space that has at most edges. The previously best known result is by Bose et al. (2011) [1]. Their -spanner is a variant of the Yao graph and has at most edges. Our new spanner is also a variant of the Yao graph.
中文翻译:
磁盘扳手的改进结构
让 是平面中n个成对的不相交磁盘的集合。考虑任意两个磁盘D和D之间的距离的度量空间 在 是连接D和的最短线段的长度。对于任何实数,我们展示了如何获取 最多具有此度量标准空间的-spanner 边缘。先前最著名的结果是Bose等人的论文。(2011)[1]。其-spanner是Yao图的一种变体,最多具有 边缘。我们的新扳手也是Yao图形的一种变体。