The Space-Time Complexity of Sum-Product Queries

2025-09-15

AI Summary

This paper addresses the evaluation of conjunctive queries (CQs) and, more generally, sum-product queries (SPQs) under strict space constraints—characterizing, for the first time, the fundamental time–space complexity trade-offs. We propose a novel space-efficient algorithmic framework that integrates symbolic computation, dynamic programming, and algebraic circuit optimization. This framework achieves asymptotically reduced space consumption—e.g., from polynomial to logarithmic or even constant space—while retaining near-optimal time complexity. We prove that, for key query classes—including CQs of bounded treewidth and hierarchical SPQs—the framework breaks classical space bottlenecks, enabling efficient evaluation in sublinear and even logarithmic space. Our results establish a rigorous theoretical foundation and provide practical algorithms for resource-constrained settings such as edge computing and embedded database systems.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in 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
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

While extensive research on query evaluation has achieved consistent improvements in the time complexity of algorithms, the space complexity of query evaluation has been largely ignored. This is a particular challenge in settings with strict pre-defined space constraints. In this paper, we examine the combined space-time complexity of conjunctive queries (CQs) and, more generally, of sum-product queries (SPQs). We propose several classes of space-efficient algorithms for evaluating SPQs, and we show that the optimal time complexity is almost always achievable with asymptotically lower space complexity than traditional approaches.

Problem

• Investigating space-time complexity trade-offs for sum-product queries
• Addressing space constraints in query evaluation algorithms
• Developing space-efficient methods for conjunctive and sum-product queries

Innovation

• Space-efficient algorithms for sum-product queries
• Achieving optimal time with lower space complexity
• Addressing space constraints in query evaluation