A Query-Driven Approach to Space-Efficient Range Searching

2025-02-19

AI Summary

This work addresses the problem of constructing space-efficient partition trees for range search under unknown query distributions accessible only via sampling, aiming to minimize expected query cost—defined as the average number of visited nodes multiplied by per-node processing overhead. We propose a query-driven tree construction paradigm: first, we formulate node partitioning as a geometric separation problem and introduce sparse geometric separators to minimize the expected number of query “piercings”; second, we cast node routing decisions as lightweight classification tasks, accelerated in real time via shallow neural networks. Theoretically, our approach guarantees near-optimal tree construction with near-linear sample complexity. Experiments demonstrate substantial reductions in both average node accesses and end-to-end query latency, yielding significant improvements in overall query efficiency.

Technology Category

• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Intelligent Query Processing
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Semantics and Knowledge: Applications of semantic technologies for improving search, browsing, recommendation, personalization

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.

Problem

• Designing partition trees for range-searching problems.
• Optimizing performance with unknown query distributions.
• Reducing query time using sparse geometric separators.

Innovation

• Query-driven partition tree design
• Shallow neural networks for classification
• Sparse geometric separators optimization