We show that $n$ real numbers can be stored in a constant number of real numbers such that each original real number can be fetched in $O(\log n)$ time. Although our result has implications for many computational geometry problems, we show here, combined with Han's $O(n\sqrt{\log n})$ time real number sorting algorithm [3, arXiv:1801.00776], we can improve the complexity of Kirkpatrick's point location algorithm [8] to $O(n\sqrt{\log n})$ preprocessing time, a constant number of real numbers for storage and $O(\log n)$ point location time. Kirkpatrick's algorithm uses $O(n\log n)$ preprocessing time, $O(n)$ storage and $O(\log n)$ point location time. The complexity results in Kirkpatrick's algorithm was the previous best result. Although Lipton and Tarjan's algorithm [10] predates Kirkpatrick's algorithm and has the same complexity, Kirkpatrick's algorithm is simpler and has a better structure. This paper can be viewed as a companion paper of paper [3, arXiv:1801.00776].

翻译：我们证明$n$个实数可被存储于常数个实数中，使得每个原始实数可在$O(\log n)$时间内获取。尽管该结果对许多计算几何问题具有启发意义，但本文聚焦于：结合韩的$O(n\sqrt{\log n})$时间实数排序算法[3, arXiv:1801.00776]，可将Kirkpatrick点定位算法[8]的复杂度优化至$O(n\sqrt{\log n})$预处理时间、常数个实数的存储空间以及$O(\log n)$点定位时间。Kirkpatrick算法原时间复杂度为$O(n\log n)$预处理时间、$O(n)$存储空间及$O(\log n)$点定位时间，该复杂度此前为最优结果。尽管Lipton与Tarjan的算法[10]早于Kirkpatrick算法且具有相同复杂度，但Kirkpatrick算法更简洁且结构更优。本文可视作论文[3, arXiv:1801.00776]的姊妹篇。