静态最优变换及其在平面点定位中的应用
A Static Optimality Transformation with Applications to Planar Point Location
摘要：
在过去的十年中，已经有几种数据结构，给定平面细分和平面上的概率分布，提供了一种用于回答针对分布进行微调的点定位查询的方法。所有这些方法都受到必须事先知道查询分布的要求的影响。提出了一种新的平面三角网点定位查询数据结构。我们的结构是渐进的最佳结构一样快，但它不需要事先的查询信息。这是从Knuth的最优二叉搜索树（1971年发现）到Sleator和Tarjan在1985年的splay树的2D模拟。虽然前者需要知道查询分布，后者是静态最优的。这意味着我们可以适应查询序列，并实现与最佳静态结构相同的渐近性能，而不需要任何额外的信息。
英文摘要：
Over the last decade, there have been several data structures that, given a planar subdivision and a probability distribution over the plane, provide a way for answering point location queries that is fine-tuned for the distribution. All these methods suffer from the requirement that the query distribution must be known in advance. We present a new data structure for point location queries in planar triangulations. Our structure is asymptotically as fast as the optimal structures, but it requires no prior information about the queries. This is a 2D analogue of the jump from Knuth's optimum binary search trees (discovered in 1971) to the splay trees of Sleator and Tarjan in 1985. While the former need to know the query distribution, the latter are statically optimal. This means that we can adapt to the query sequence and achieve the same asymptotic performance as an optimum static structure, without needing any additional information.
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