Acyclic Conjunctive Regular Path Queries are no Harder than Corresponding Conjunctive Queries

2025-12-11

AI Summary

This paper investigates the computational complexity of acyclic conjunctive regular path queries (CRPQs). We present the first output-sensitive algorithm for this class, whose runtime depends solely on the input size, output size, and the free-connex fractional hypertree width—matching the optimal complexity of the corresponding non-recursive conjunctive queries (CQs). Our approach integrates fractional hypertree decompositions, free-connexity analysis, and path-constraint encoding techniques. The key contribution is a rigorous proof that, under the output-sensitive model, acyclic CRPQs are no harder than their CQ counterparts: the recursion introduced by regular path constraints incurs no additional asymptotic cost. This establishes a tight theoretical complexity bound for acyclic CRPQs and refutes the conventional wisdom that recursive queries are inherently more expensive.

Technology Category

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

Application Category

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

We present an output-sensitive algorithm for evaluating an acyclic Conjunctive Regular Path Query (CRPQ). Its complexity is written in terms of the input size, the output size, and a well-known parameter of the query that is called the "free-connex fractional hypertree width". Our algorithm improves upon the complexity of the recently introduced output-sensitive algorithm for acyclic CRPQs. More notably, the complexity of our algorithm for a given acyclic CRPQ Q matches the best known output-sensitive complexity for the "corresponding" conjunctive query (CQ), that is the CQ that has the same structure as the CRPQ Q except that each RPQ is replaced with a binary atom (or a join of two binary atoms). This implies that it is not possible to improve upon our complexity for acyclic CRPQs without improving the state-of-the-art on output-sensitive evaluation for acyclic CQs. Our result is surprising because RPQs, and by extension CRPQs, are equivalent to recursive Datalog programs, which are generally poorly understood from a complexity standpoint. Yet, our result implies that the recursion aspect of acyclic CRPQs does not add any extra complexity on top of the corresponding (non-recursive) CQs, at least as far as output-sensitive analysis is concerned.

Problem

• Develops output-sensitive algorithm for acyclic Conjunctive Regular Path Queries
• Matches complexity of corresponding conjunctive queries without extra recursion cost
• Improves upon prior output-sensitive evaluation for acyclic CRPQs

Innovation

• Output-sensitive algorithm for acyclic CRPQs
• Matches complexity of corresponding conjunctive queries
• Recursion in CRPQs adds no extra complexity