1. Complexity of conjunctive regular path query homomorphisms
- Author
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Florent R. Madelaine, Florent Foucaud, Lhouari Nourine, Gaétan Richard, Laurent Beaudou, Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes (LIMOS), SIGMA Clermont (SIGMA Clermont)-Université d'Auvergne - Clermont-Ferrand I (UdA)-Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Blaise Pascal - Clermont-Ferrand 2 (UBP), Laboratoire d'Algorithmique Complexité et Logique (LACL), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), Equipe AMACC - Laboratoire GREYC - UMR6072, Groupe de Recherche en Informatique, Image et Instrumentation de Caen (GREYC), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Normandie Université (NU)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), IFCAM project 'Applications of graph homomorphisms' (MA/IFCAM/18/39)., ANR-17-CE40-0022,HOSIGRA,Homomorphismes de graphes signés(2017), ANR-16-IDEX-0001,CAP 20-25,CAP 20-25(2016), and Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Université d'Auvergne - Clermont-Ferrand I (UdA)-SIGMA Clermont (SIGMA Clermont)-Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)
- Subjects
FOS: Computer and information sciences ,Computer Science - Logic in Computer Science ,Discrete Mathematics (cs.DM) ,computer.internet_protocol ,Computer science ,Formal Languages and Automata Theory (cs.FL) ,EXPTIME ,Computer Science - Formal Languages and Automata Theory ,0102 computer and information sciences ,computer.software_genre ,01 natural sciences ,Combinatorics ,Computer Science - Databases ,Regular expression ,0101 mathematics ,Computer Science::Databases ,ComputingMilieux_MISCELLANEOUS ,XPath ,Graph database ,[INFO.INFO-DB]Computer Science [cs]/Databases [cs.DB] ,010102 general mathematics ,InformationSystems_DATABASEMANAGEMENT ,[INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO] ,Digraph ,Databases (cs.DB) ,Logic in Computer Science (cs.LO) ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,010201 computation theory & mathematics ,Path (graph theory) ,Regular graph ,Homomorphism ,computer ,Computer Science::Formal Languages and Automata Theory ,Computer Science - Discrete Mathematics - Abstract
A graph database is a digraph whose arcs are labeled with symbols from a fixed alphabet. A regular graph pattern (RGP) is a digraph whose edges are labeled with regular expressions over the alphabet. RGPs model navigational queries for graph databases called conjunctive regular path queries (CRPQs). A match of a CRPQ in the database is witnessed by a special navigational homomorphism of the corresponding RGP to the database. We study the complexity of deciding the existence of a homomorphism between two RGPs. Such homomorphisms model a strong type of containment between the two corresponding CRPQs. We show that this problem can be solved by an EXPTIME algorithm (while general query containmement in this context is EXPSPACE-complete). We also study the problem for restricted RGPs over a unary alphabet, that arise from some applications like XPath or SPARQL. For this case, homomorphism-based CRPQ containment is in NP. We prove that certain interesting cases are in fact polynomial-time solvable., 15 pages. Short version appeared in the proceedings of the 15th Conference on Computability in Europe (CIE 2019)
- Published
- 2023