半动态矩形交查询算法

SEMI-DYNAMIC RECTANGLE INTERSECTION SEARCHING ALGORITHM

本文讨论了动态矩形交查询算法.文中介绍了两个半动态矩形查询的新算法，它们分别基于一维数据结构和二维数据结构.一维查询算法的查询时间复杂度是O（logM＋k′），更新时间复杂度是O（logMlogn），空间复杂度是O（nlogM）.二维查询算法的查询时间复杂度是O（log2M＋k），更新时间复杂度是O（log2Mlogn），空间复杂度是O（nlog2M）.本文分别实现了这两个算法，通过对它们的性能进行比较，发现一维查询算法是一种高效、实用的算法.

This paper introduces a solution to dynamic rectangle intersection searching problem. There are two semi-dynamic algorithms which are based on 1-dimensional data structure and 2-dimensional data structure respectively. The computational complexity of 1-D searching algorithm is as follows: query time O (logM + k'), update time O(logANogn), space O(nlogM). The computational complexity of 2-D searching algorithm is as follows: query time O(log2M+k), update time O(log2Mlogn), space O(nlog2M).The two algorithms are implemented respectively. With an experimental comparison, the authors found that 1-D searching algorithm is far better than 2-D searching algorithm.