Resilience for Regular Path Queries: Towards a Complexity Classification

2024-12-12

arXiv.org

AI Summary

This paper investigates the resilience computation problem for Regular Path Queries (RPQs) over graph databases—i.e., the minimum number of facts whose deletion falsifies an existential RPQ result. The central objective is to classify the computational complexity of RPQ resilience with respect to the regular language (L) defining the RPQ. The authors establish the first precise complexity characterization: they prove that joint complexity is polynomial-time solvable when (L) is a *local* language, and rigorously show NP-hardness under data complexity for several canonical non-local languages—including finite languages containing repeated letters, four-legged languages, and non-local languages admitting neutral letters. This work yields an essentially complete complexity dichotomy and, for the first time, systematically links fundamental formal language properties—locality, star-freeness, and presence of neutral letters—to robustness analysis of graph queries, substantially advancing the theoretical foundations of query resilience in graph databases.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Intelligent Query Processing
• Natural Language Processing: Safety and Robustness

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

The resilience problem for a query and an input set or bag database is to compute the minimum number of facts to remove from the database to make the query false. In this paper, we study how to compute the resilience of Regular Path Queries (RPQs) over graph databases. Our goal is to characterize the regular languages $L$ for which it is tractable to compute the resilience of the existentially-quantified RPQ built from $L$. We show that computing the resilience in this sense is tractable (even in combined complexity) for all RPQs defined from so-called local languages. By contrast, we show hardness in data complexity for RPQs defined from the following language classes (after reducing the languages to eliminate redundant words): all finite languages featuring a word containing a repeated letter, and all languages featuring a specific kind of counterexample to being local (which we call four-legged languages). The latter include in particular all languages that are not star-free. Our results also imply hardness for all non-local languages with a so-called neutral letter. We last highlight some remaining obstacles towards a full dichotomy.

Problem

• Compute resilience for Regular Path Queries in graph databases
• Identify tractable regular languages for resilience computation
• Classify complexity for non-local and finite language RPQs

Innovation

• Tractable resilience for local language RPQs
• Hardness for finite languages with repeats
• Hardness for non-local four-legged languages