A Query-Driven Approach to Space-Efficient Range Searching

TL;DR

This paper introduces a query-driven method for constructing space-efficient partition trees for range searching, optimizing expected query performance using sampling and classification techniques.

Contribution

It presents a novel approach combining sampling, classification, and sparse separators to build efficient, query-optimized partition trees for range searching.

Findings

Near-linear sample of queries suffices for near-optimal trees

Classification with neural networks improves query times

Sparse geometric separators reduce query complexity

Abstract

We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle, and must be selected such that it optimizes a meaningful performance parameter on expectation. Our first contribution is to show that a near-linear sample of queries allows the construction of a partition tree with a near-optimal expected number of nodes visited during querying. We enhance this approach by treating node processing as a classification problem, leveraging fast classifiers like shallow neural networks to obtain experimentally efficient query times. Our second contribution is to develop partition trees using sparse geometric separators. Our preprocessing algorithm, based on a sample of queries, builds a balanced tree with nodes associated with separators that minimize query stabs on expectation; this yields both fast processing of each node and a small number of visited nodes, significantly reducing query time.