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The Complexity of Resilience for Digraph Queries

Authors Manuel Bodirsky , Žaneta Semanišinová

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ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Complexity theory and logic
  • Theory of computation → Database query processing and optimization (theory)
Keywords
  • valued constraints
  • unions of conjunctive queries
  • resilience
  • computational complexity
  • pp-constructions

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Abstract

We prove a complexity dichotomy for the resilience problem for unions of conjunctive digraph queries (i.e., for existential positive sentences over the signature {R} of directed graphs). Specifically, for every union μ of conjunctive digraph queries, the following problem is in P or NP-complete: given a directed multigraph G and a natural number u, can we remove u edges from G so that G ⊧ ¬ μ? In fact, we verify a more general dichotomy conjecture from [Bodirsky et al., 2024] for all resilience problems in the special case of directed graphs, and show that for such unions of queries μ there exists a countably infinite (`dual') valued structure Δ_μ which either primitively positively constructs 1-in-3-3-SAT, and hence the resilience problem for μ is NP-complete by general principles, or has a pseudo cyclic canonical fractional polymorphism, and the resilience problem for μ is in P.

Cite As Get BibTex

Manuel Bodirsky and Žaneta Semanišinová. The Complexity of Resilience for Digraph Queries. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.STACS.2026.15

Author Details

Manuel Bodirsky
  • Institut für Algebra, TU Dresden, Germany
Žaneta Semanišinová
  • Institute of Discrete Mathematics and Geometry, TU Wien, Austria

Funding

  • Bodirsky, Manuel: The author has been funded by the European Research Council (Project POCOCOP, ERC Synergy Grant 101071674) and by the DFG (Project FinHom, Grant 467967530). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.
  • Semanišinová, Žaneta: The author has been funded by the European Research Council (Project POCOCOP, ERC Synergy Grant 101071674). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. This research was funded in whole or in part by the Austrian Science Fund (FWF) 10.55776/ESP6949724.

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