Abstract
Graph databases are currently one of the most popular paradigms for storing data. One of the key conceptual differences between graph and relational databases is the focus on navigational queries that ask whether some nodes are connected by paths satisfying certain restrictions. This focus has driven the definition of several different query languages and the subsequent study of their fundamental properties. We define the graph query language of Regular Queries, which is a natural extension of unions of conjunctive 2-way regular path queries (UC2RPQs) and unions of conjunctive nested 2-way regular path queries (UCN2RPQs). Regular queries allow expressing complex regular patterns between nodes. We formalize regular queries as nonrecursive Datalog programs extended with the transitive closure of binary predicates. This language has been previously considered, but its algorithmic properties are not well understood. Our main contribution is to show elementary tight bounds for the containment problem for regular queries. Specifically, we show that this problem is 2Expspace-complete. For all extensions of regular queries known to date, the containment problem turns out to be non-elementary. Together with the fact that evaluating regular queries is not harder than evaluating UCN2RPQs, our results show that regular queries achieve a good balance between expressiveness and complexity, and constitute a well-behaved class that deserves further investigation.
Similar content being viewed by others
Notes
1 These programs are sometimes referred to as stratified linear programs, or piecewise linear Programs [45].
References
Abiteboul, S., Hull, R., Vianu, V.: Foundations of databases Addison-Wesley (1995)
Angles, R., Gutierrez, C.: Survey of graph database models. ACM Comput. Surv 40(1) (2008)
Arenas, M., Gutierrez, C., Miranker, D.P., Pérez, J., Sequeda, J.F.: Querying semantic data on the web? ACM SIGMOD Rec 41(4), 6–17 (2013)
Arenas, M., Pérez, J.: Querying semantic web data with sparql. In: PODS, pp 305–316 (2011)
Barcelo, P., Libkin, L., Lin, A.W., Wood, P.T.: Expressive languages for path queries over graph-structured data. ACM TODS 37(4), 31 (2012)
Barceló, P., Pérez, J., Reutter, J.L.: Relative expressiveness of nested regular expressions. In: AMW, pp 180–195 (2012)
Barcelo, P., Romero, M., Vardi, M.Y.: Semantic acyclicity on graph databases. In: PODS, pp 237–248 (2013)
Barceló Baeza, P.: Querying graph databases. In: PODS, pp 175–188 (2013)
Bienvenu, M., Calvanese, D., Ortiz, M., Simkus, M.: Nested regular path queries in description logics. In: KR (2014)
Bienvenu, M., Ortiz, M., Šimkus, M.: Conjunctive regular path queries in lightweight description logics. In: IJCAI, pp 761–767 (2013)
Bienvenu, M., Ortiz, M., Šimkus, M.: Navigational queries based on frontier-guarded datalog Preliminary results. In: Alberto Mendelzon International Workshop on Foundations of Data Management, p 162 (2015)
Bourhis, P., Krötzsch, M., Rudolph, S.: How to best nest regular path queries. In: Description Logics (2014)
Bourhis, P., Krötzsch, M., Rudolph, S.: Query containment for highly expressive datalog fragments. preprint arXiv: 1406.7801 (2014)
Bourhis, P., Krötzsch, M., Rudolph, S.: Reasonable highly expressive query languages. In: IJCAI, pp 2826–2832 (2015)
Buneman, P.: Semistructured data. In: Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems, pp 117–121 (1997)
Buneman, P., Davidson, S., Hillebrand, G., Suciu, D.: A query language and optimization techniques for unstructured data. ACM SIGMOD Rec 25(2), 505–516 (1996)
Calvanese, D., De Giacomo, G., Lenzerini, M., Vardi, M.: Containment of conjunctive regular path queries with inverse. In: 7th International Conference on Principles of Knowledge Representation and Reasoning (KR), pp 176–185 (2000)
Calvanese, D., De Giacomo, G., Lenzerini, M., Vardi, M.: Rewriting of regular expressions and regular path queries. J. Comput. Syst. Sci 64(3), 443–465 (2002)
Calvanese, D., De Giacomo, G., Vardi, M.Y.: Decidable containment of recursive queries. Theor. Comput. Sci 336(1), 33–56 (2005)
Calvanese, D., Giacomo, G.D., Lenzerini, M.: Conjunctive query containment and answering under description logic constraints. ACM Trans. Comput. Log 9(3) (2008)
Chandra, A.K., Merlin, P.M.: Optimal implementation of conjunctive queries in relational data bases. In: Proceedings of the ninth annual ACM symposium on Theory of computing, pp 77–90 (1977)
Chaudhuri, S., Krishnamurthy, R., Potamianos, S., Shim, K.: Optimizing queries with materialized views. In: 2013 IEEE 29Th International Conference on Data Engineering (ICDE), p 1995
Chaudhuri, S., Vardi, M.Y.: On the equivalence of recursive and nonrecursive datalog programs. In: Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems, pp 55–66 (1992)
Chekuri, C., Rajaraman, A.: Conjunctive query containment revisited. Theor. Comput. Sci 239(2), 211–229 (2000)
Consens, M., Mendelzon, A.: Graphlog: A visual forMalism for real life recursion. In: 9th ACM Symposium on Principles of Database Systems (PODS), pp 404–416 (1990)
Courcelle, B.: The monadic second-order logic of graphs. i. recognizable sets of finite graphs. Inf. Comput 85(1), 12–75 (1990)
Courcelle, B.: Recursive queries and context-free graph grammars. Theor. Comput. Sci 78(1), 217–244 (1991)
Cruz, I., Mendelzon, A., Wood, P.: A graphical query language supporting recursion. In: ACM Special Interest Group on Management of Data 1987 Annual Conference (SIGMOD), pp 323–330 (1987)
Dalmau, V., Kolaitis, P.G., Vardi, M.Y.: Constraint satisfaction, bounded treewidth, and finite-variable logics. In: Principles and Practice of Constraint Programming-CP 2002, pp 310–326. Springer (2002)
Fagin, R., Vardi, M.Y.: The theory of data dependenciesan overview. In: Automata, Languages and Programming, pp 1–22. Springer (1984)
Fan, W.: Graph pattern matching revised for social network analysis. In: Proceedings of the 15th International Conference on Database Theory, pp 8–21 (2012)
Fernandez, M., Florescu, D., Levy, A., Suciu, D.: Verifying integrity constraints on web sites. In: IJCAI, vol. 99, pp 614–619 (1999)
Fletcher, G.H., Gyssens, M., Leinders, D., Surinx, D., Van den Bussche, J., Van Gucht, D., Vansummeren, S., Wu, Y.: Relative expressive power of navigational querying on graphs. Inf. Sci 298, 390–406 (2015)
Florescu, D., Levy, A.Y., Mendelzon, A.O.: Database techniques for the world-wide web: A survey. SIGMOD Rec 27(3), 59–74 (1998)
Friedman, M., Levy, A.Y., Millstein, T.D., etal: Navigational plans for data integration. AAAI/IAAI 1999, 67–73 (1999)
Imielinski, T., Lipski, W.: Incomplete information in relational databases. J. ACM 31(4), 761–791 (1984)
Kostylev, E.V., Reutter, J.L., Vrgoc, D.: Containment of data graph queries. In: ICDT, pp 131–142 (2014)
Lacroix, Z., Murthy, H., Naumann, F., Raschid, L.: Links and paths through life sciences data sources. In: Data Integration in the Life Sciences, pp 203–211. Springer (2004)
Libkin, L., Martens, W., Vrgoč, D.: Querying graph databases with xpath. In: Proceedings of the 16th International Conference on Database Theory, pp 129–140 (2013)
Libkin, L., Reutter, J., Vrgoč, D.: Trial for rdf: adapting graph query languages for rdf data. In: PODS, pp 201–212 (2013)
Pérez, J., Arenas, M., Gutierrez, C.: nSPARQL: A navigational language for RDF. J. Web Semant 8(4), 255–270 (2010)
Reutter, J.L., Romero, M., Vardi, M.Y.: Regular queries on graph databases. In: 18th International Conference on Database Theory (ICDT 2015), vol. 31, pp 177–194 (2015)
Rudolph, S., Krötzsch, M.: Flag & check: Data access with monadically defined queries. In: Proceedings of the 32nd symposium on Principles of database systems, pp 151–162 (2013)
Sagiv, Y., Yannakakis, M.: Equivalences among relational expressions with the union and difference operators. J. ACM (JACM) 27(4), 633–655 (1980)
Ullman, J.D.: Principles of database and Knowledge-Base systems computer science press (1989)
Vorobyov, S., Voronkov, A.: Complexity of nonrecursive logic programs with complex values. In: PODS, pp 244–253 (1998)
Acknowledgments
We’d like to thank Pablo Barceló for helpful discussions on regular queries. The third author is grateful to Vincent Jugé for early discussions on containment of regular queries. First and second authors are supported by the Millennium Nucleus Center for Semantic Web Research Grant NC120004, and first author also by Fondecyt Iniciación grant 11130648.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Reutter, J.L., Romero, M. & Vardi, M.Y. Regular Queries on Graph Databases. Theory Comput Syst 61, 31–83 (2017). https://doi.org/10.1007/s00224-016-9676-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00224-016-9676-2