Real-world point sets tend to be clustered, so using a machine word for each point is wasteful. In this paper we first show how a compact representation of quadtrees using $O (1)$ bits per node can break this bound on clustered point sets, while offering efficient range searches. We then describe a new compact quadtree representation based on heavy path decompositions, which supports queries faster than previous compact structures. We present experimental evidence showing that our structure is competitive in practice.

翻译：现实世界的点群往往会聚集在一起, 所以对每个点使用一个机器词是浪费的。 在本文中, 我们首先展示了使用每个节点的一元一元一元一元的二次树的缩压代表可以如何打破这个框框, 同时提供高效的射程搜索。 我们然后描述一个新的基于重路径分解的四方代表, 它支持比先前的紧凑结构更快的查询。 我们提出实验性证据表明我们的结构在实践中具有竞争力 。