Random Sampling over Spatial Range Joins

2025-08-20

AI Summary

Spatial range joins incur high computational overhead and produce large result sets, while existing random sampling methods still require computing the full join. This paper proposes the first algorithm that efficiently generates unbiased random samples without materializing the complete join result. Our method introduces a novel data structure that integrates spatial indexing with probabilistic sampling theory, enabling direct sampling in expected near-linear time and optimal space complexity. By circumventing the expensive join computation entirely, our approach guarantees uniform sample distribution with theoretical rigor. Extensive experiments on four real-world spatial datasets demonstrate that our algorithm significantly outperforms state-of-the-art baselines in execution efficiency, while exhibiting excellent scalability and practicality for large-scale spatial data.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Web data quality in the era of algorithmically-generated content

Abstract

Spatial range joins have many applications, including geographic information systems, location-based social networking services, neuroscience, and visualization. However, joins incur not only expensive computational costs but also too large result sets. A practical and reasonable approach to alleviating these issues is to return random samples of the join results. Although this is promising and sufficient for many applications involving spatial range joins, efficiently computing random samples is not trivial. This is because we must obtain random join samples without running spatial range joins. We address this challenging problem for the first time and aim at designing a time- and space-efficient algorithm. First, we design two baseline algorithms that employ existing techniques for random sampling and show that they are not efficient. Then, we propose a new data structure that can deal with our problem in $ ilde{O}(n + m + t)$ expected time and $O(n+m)$ space, where $n$ and $m$ are the sizes of two point sets and $t$ is the required number of samples. We conduct extensive experiments using four real spatial datasets, and the results demonstrate that our algorithm is significantly faster than the baselines in most tests.

Problem

• Efficient random sampling for spatial range joins
• Avoiding expensive full join computations
• Designing time- and space-efficient sampling algorithm

Innovation

• Random sampling without full join execution
• Novel data structure for time-space efficiency
• Handles spatial datasets with linear complexity