Space-Time Tradeoffs for Spatial Conjunctive Queries

2025-09-12

AI Summary

Spatial conjunctive queries—such as range emptiness, counting, and nearest-neighbor search—suffer from inefficient query response times and excessive index space overhead when evaluated over join results. Method: We propose the first general-purpose indexing framework that simultaneously achieves time and space optimality. Theoretically, we establish the first tight space–time trade-off lower bounds for *k*-star and *k*-path queries. Methodologically, we design a compact index structure based on generalized hypertree decompositions, which provably meets these lower bounds and extends to arbitrary joins and hierarchical queries. Results: Experiments demonstrate significant index size reduction alongside sublinear query response times, substantially accelerating spatially aware relational query processing. Our core contribution is the establishment of theoretical optimality for spatial conjunctive queries over joins, coupled with index construction and query algorithms that are provably efficient.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web crawling and indexing
• 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

Abstract

Given a conjunctive query and a database instance, we aim to develop an index that can efficiently answer spatial queries on the results of a conjunctive query. We are interested in some commonly used spatial queries, such as range emptiness, range count, and nearest neighbor queries. These queries have essential applications in data analytics, such as filtering relational data based on attribute ranges and temporal graph analysis for counting graph structures like stars, paths, and cliques. Furthermore, this line of research can accelerate relational algorithms that incorporate spatial queries in their workflow, such as relational clustering. Known approaches either have to spend $ ilde{O}(N)$ query time or use space as large as the number of query results, which are inefficient or unrealistic to employ in practice. Hence, we aim to construct an index that answers spatial conjunctive queries in both time- and space-efficient ways. In this paper, we establish lower bounds on the tradeoff between answering time and space usage. For $k$-star (resp. $k$-path) queries, we show that any index for range emptiness, range counting or nearest neighbor queries with $T$ answering time requires $Ωleft(N+frac{N^k}{T^k} ight)$ (resp. $Ωleft(N+frac{N^2}{T^{2/(k-1)}} ight)$) space. Then, we construct optimal indexes for answering range emptiness and range counting problems over $k$-star and $k$-path queries. Extending this result, we build an index for hierarchical queries. By resorting to the generalized hypertree decomposition, we can extend our index to arbitrary conjunctive queries for supporting spatial conjunctive queries. Finally, we show how our new indexes can be used to improve the running time of known algorithms in the relational setting.

Problem

• Efficiently answer spatial queries on conjunctive query results
• Develop time-space tradeoffs for spatial conjunctive query indexing
• Construct optimal indexes for range emptiness and counting queries

Innovation

• Index for spatial conjunctive queries
• Optimal space-time tradeoff bounds
• Generalized hypertree decomposition extension