Minimizing Conjunctive Regular Path Queries

2025-04-01

AI Summary

This paper investigates the minimization problem for conjunctive regular path queries (CRPQs) and their unions (UCRPQs): given a query $ Q $ and an integer $ k $, determine whether $ Q $ is equivalent to a simpler query with at most $ k $ atoms—where CRPQ size is measured by atom count, and UCRPQ size by the maximum atom count across its disjunctive branches. We establish, for the first time, the decidability of this problem. Our method leverages automata-theoretic semantics and constructs lower approximations to analyze query equivalence. We prove a 2ExpSpace upper bound and an ExpSpace lower bound for CRPQ minimization, and show that UCRPQ minimization is ExpSpace-complete. Under restrictions to simple regular expressions, we further obtain a $Pi^p_2$-completeness characterization. These results provide both a theoretical foundation and precise complexity characterizations for optimizing path queries in graph databases.

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
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We study the minimization problem for Conjunctive Regular Path Queries (CRPQs) and unions of CRPQs (UCRPQs). This is the problem of checking, given a query and a number $k$, whether the query is equivalent to one of size at most $k$. For CRPQs we consider the size to be the number of atoms, and for UCRPQs the maximum number of atoms in a CRPQ therein, motivated by the fact that the number of atoms has a leading influence on the cost of query evaluation. We show that the minimization problem is decidable, both for CRPQs and UCRPQs. We provide a 2ExpSpace upper-bound for CRPQ minimization, based on a brute-force enumeration algorithm, and an ExpSpace lower-bound. For UCRPQs, we show that the problem is ExpSpace-complete, having thus the same complexity as the classical containment problem. The upper bound is obtained by defining and computing a notion of maximal under-approximation. Moreover, we show that for UCRPQs using the so-called"simple regular expressions"consisting of concatenations of expressions of the form $a^+$ or $a_1 + dotsb + a_k$, the minimization problem becomes $Pi^p_2$-complete, again matching the complexity of containment.

Problem

• Minimizing size of Conjunctive Regular Path Queries (CRPQs)
• Deciding equivalence of queries with size constraints
• Analyzing complexity of minimization for CRPQs and UCRPQs

Innovation

• Decidable minimization for CRPQs and UCRPQs
• Brute-force enumeration for CRPQ minimization
• Maximal under-approximation for UCRPQs