Resilience for Regular Path Queries: Towards a Complexity Classification
Antoine Amarilli, Wolfgang Gatterbauer, Neha Makhija, Mikaël Monet, Martín Muñoz
TL;DR
This work investigates resilience for Regular Path Queries (RPQs) over graph databases, aiming to classify the regular languages L by the tractability of computing resilience for existentially quantified RPQs defined by L. It introduces a MinCut-based reduction framework for local languages (RO-εNFA/Read-Once automata) and proves PTIME resilience for these languages, while establishing NP-hardness for broad non-local families such as four-legged languages and finite infix-free languages containing a repeated letter. The paper further identifies tractable non-local classes (bipartite chain languages and one-dangling languages) and develops a spectrum of hardness gadgets, condensed hypergraphs of matches, and flow-based reductions to capture the complexity boundary. Overall, the authors provide a substantial, language-theoretic dichotomy-like landscape for RPQ resilience, with several open problems and directions for extending to non-Boolean RPQs and other semantics.
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 show tractability for some classes of non-local languages, namely the so-called bipartite chain languages and one-dangling languages, and highlight some remaining obstacles towards a full dichotomy.