Faster Compressed Quadtrees

TL;DR

This paper introduces a new compact quadtree representation that efficiently handles clustered point sets and supports faster range queries, with practical performance demonstrated through experiments.

Contribution

A novel compact quadtree structure based on heavy path decompositions that improves query speed over previous methods for clustered data.

Findings

Breaks the (1) bits per node bound on clustered point sets

Supports faster range searches than previous compact structures

Experimental results show practical competitiveness

Abstract

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 $\Oh{1}$ 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.