论文标题
最接近的问题查询和最小重量查询相当于正方形
Closest-Pair Queries and Minimum-Weight Queries are Equivalent for Squares
论文作者
论文摘要
让$ s $是飞机上的一组$ n $加权点，让$ r $为飞机中的查询范围。在最接近的一对问题中，我们想报告集合$ r \ cap s $中的最接近的一对。在最小重量问题的范围内，我们想报告集合$ r \ cap s $中任何点的最小重量。我们表明，对于具有$ω（\ log n）$查询时间的数据结构的查询范围，这两个查询问题是等效的。结果，我们获得了带有正方形的最接近对范围的查询的新数据结构。
Let $S$ be a set of $n$ weighted points in the plane and let $R$ be a query range in the plane. In the range closest pair problem, we want to report the closest pair in the set $R \cap S$. In the range minimum weight problem, we want to report the minimum weight of any point in the set $R \cap S$. We show that these two query problems are equivalent for query ranges that are squares, for data structures having $Ω(\log n)$ query times. As a result, we obtain new data structures for range closest pair queries with squares.
