Abstract
A graph database is a digraph whose arcs are labelled with symbols from a fixed alphabet. A regular graph pattern (RGP) is a digraph whose edges are labelled with regular expressions over the alphabet. RGPs model navigational queries for graph databases, more precisely, conjunctive regular path queries. A match of a navigational RGP query in the database is witnessed by a special navigational homomorphism of the 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 two navigational RGP queries. We show that this problem can be solved by an EXPTIME algorithm (while general query containment 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, and prove that certain interesting cases are polynomial-time solvable.
The authors acknowledge the support received from the Agence Nationale de la Recherche of the French government throught the program “Investissements d’Avenir” (16-IDEX-0001 CAP 20-25), the IFCAM project “Applications of graph homomorphisms” (MA/IFCAM/18/39), and by the ANR project HOSIGRA (ANR-17-CE40-0022).
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Notes
- 1.
There exist more complicated examples where, furthermore, the two non-isomorphic n-cores have the same size.
- 2.
This is not true for all acyclic RGPs: there are trees T such that Hom(T) is NP-hard [6]. Thus, for the corresponding \(\{a\}\)-RGP Q(T), RGPHom(Q(T)) is NP-hard.
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Beaudou, L., Foucaud, F., Madelaine, F., Nourine, L., Richard, G. (2019). Complexity of Conjunctive Regular Path Query Homomorphisms. In: Manea, F., Martin, B., Paulusma, D., Primiero, G. (eds) Computing with Foresight and Industry. CiE 2019. Lecture Notes in Computer Science(), vol 11558. Springer, Cham. https://doi.org/10.1007/978-3-030-22996-2_10
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