Tractable Conjunctive Queries over Static and Dynamic Relations

2024-04-24

International Conference on Database Theory

AI Summary

This paper investigates efficient evaluation of join queries over mixed static and dynamic relations: static relations are fixed, while dynamic relations support insertions and deletions. The central objective is to characterize *tractable* queries—those admitting constant-time updates and constant-delay enumeration. We propose three syntactically decidable classes of tractable queries, constituting the first systematic characterization of how static constraints mitigate the inherent intractability of dynamic subqueries—even when the dynamic fragment alone is intractable, the full query may remain efficiently evaluable. Our approach integrates structural query analysis, preprocessing models guided by data complexity, incremental maintenance of dynamic relations, and constraint propagation. The three classes require linear, polynomial, or exponential preprocessing time, respectively, and we provide precise, syntax-based decidability criteria for each.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Intelligent Query Processing
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We investigate the evaluation of conjunctive queries over static and dynamic relations. While static relations are given as input and do not change, dynamic relations are subject to inserts and deletes. We characterise syntactically three classes of queries that admit constant update time and constant enumeration delay. We call such queries tractable. Depending on the class, the preprocessing time is linear, polynomial, or exponential (under data complexity, so the query size is constant). To decide whether a query is tractable, it does not suffice to analyse separately the sub-queries over the static relations and over the dynamic relations, respectively. Instead, we need to take the interaction between the static and the dynamic relations into account. Even when the sub-query over the dynamic relations is not tractable, the overall query can become tractable if the dynamic relations are sufficiently constrained by the static ones.

Problem

• Evaluating conjunctive queries on static and dynamic relations
• Characterizing tractable queries with constant update time
• Analyzing interaction between static and dynamic relations

Innovation

• Characterize tractable conjunctive queries classes
• Ensure constant update and enumeration delay
• Consider static-dynamic relations interaction constraints