排序约旦序列在线性时间使用水平链接搜索树

Q4 Mathematics
Kurt Hoffmann, Kurt Mehlhorn, Pierre Rosenstiehl, Robert E. Tarjan
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引用次数: 121

摘要

对于任意位置与x轴相切的平面上的约当曲线C,设x1, x2,…,xn为C与x轴交点的横坐标,按点在C上出现的顺序排列。我们称x1, x2,…,xn为约当序列。本文描述了一种O(n)时间的Jordan序列识别和排序算法。排序这种序列的问题出现在计算几何和计算地理中。我们的算法基于将识别和排序问题简化为列表分割问题。为了解决列表分割问题,我们使用层次链接搜索树。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Sorting jordan sequences in linear time using level-linked search trees

For a Jordan curve C in the plane nowhere tangent to the x axis, let x1, x2,…, xn be the abscissas of the intersection points of C with the x axis, listed in the order the points occur on C. We call x1, x2,…, xn a Jordan sequence. In this paper we describe an O(n)-time algorithm for recognizing and sorting Jordan sequences. The problem of sorting such sequences arises in computational geometry and computational geography. Our algorithm is based on a reduction of the recognition and sorting problem to a list-splitting problem. To solve the list-splitting problem we use level-linked search trees.

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来源期刊
信息与控制
信息与控制 Mathematics-Control and Optimization
CiteScore
1.50
自引率
0.00%
发文量
4623
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