A Query-Driven Approach to Space-Efficient Range Searching
This work addresses efficient range searching in computational geometry, offering incremental improvements by integrating query sampling and machine learning techniques.
The paper tackles the problem of designing partition trees for range searching by using a query-driven approach that optimizes expected performance based on an unknown query distribution, achieving near-optimal expected node visits with near-linear query samples and significantly reducing query times through fast classifiers and sparse geometric separators.
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.