Faster Compressed Quadtrees

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.