Document Open Access Logo

Evaluation and Enumeration Problems for Regular Path Queries

Authors Wim Martens, Tina Trautner

PDF
Thumbnail PDF

File

LIPIcs.ICDT.2018.19.pdf
  • Filesize: 0.6 MB
  • 21 pages

Document Identifiers

Author Details

Wim Martens
Tina Trautner

Cite As Get BibTex

Wim Martens and Tina Trautner. Evaluation and Enumeration Problems for Regular Path Queries. In 21st International Conference on Database Theory (ICDT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 98, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ICDT.2018.19

Abstract

Regular path queries (RPQs) are a central component of graph databases. We investigate decision- and enumeration problems concerning the evaluation of RPQs under several semantics that have recently been considered: arbitrary paths, shortest paths, and simple paths. Whereas arbitrary and shortest paths can be enumerated in polynomial delay, the situation is much more intricate for simple paths. For instance, already the question if a given graph contains a simple path of a certain length has cases with highly non-trivial solutions and cases that are long-standing open problems. We study RPQ evaluation for simple paths from a parameterized complexity perspective and define a class of simple transitive expressions that is prominent in practice and for which we can prove a dichotomy for the evaluation problem. We observe that, even though simple path semantics is intractable for RPQs in general, it is feasible for the vast majority of RPQs that are used in practice. At the heart of our study on simple paths is a result of independent interest: the two disjoint paths problem in directed graphs is W[1]-hard if parameterized by the length of one of the two paths.

Subject Classification

Keywords
  • graph databases
  • regular path queries
  • regular languages
  • parameterized complexity

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Margareta Ackerman and Jeffrey Shallit. Efficient enumeration of words in regular languages. Theoretical Compututer Science (TCS), 410(37):3461-3470, 2009. Google Scholar
  2. Noga Alon, Raphael Yuster, and Uri Zwick. Color-coding. Journal of the ACM, 42(4):844-856, 1995. Google Scholar
  3. Renzo Angles, Marcelo Arenas, Pablo Barceló, Aidan Hogan, Juan L. Reutter, and Domagoj Vrgoč. Foundations of modern query languages for graph databases. ACM Computing Surveys, 50(5):68:1-68:40, 2017. Google Scholar
  4. Marcelo Arenas, Sebastián Conca, and Jorge Pérez. Counting beyond a yottabyte, or how SPARQL 1.1 property paths will prevent adoption of the standard. In International Conference on World Wide Web (WWW), pages 629-638, 2012. Google Scholar
  5. Guillaume Bagan, Angela Bonifati, and Benoît Groz. A trichotomy for regular simple path queries on graphs. In Symposium on Principles of Database Systems (PODS), pages 261-272, 2013. Google Scholar
  6. Pablo Barceló. Querying graph databases. In Symposium on Principles of Database Systems (PODS), pages 175-188, 2013. Google Scholar
  7. Andreas Björklund, Thore Husfeldt, and Sanjeev Khanna. Approximating longest directed paths and cycles. In International Colloquium on Automata, Languages and Programming (ICALP), pages 222-233, 2004. Google Scholar
  8. Angela Bonifati, Wim Martens, and Thomas Timm. An analytical study of large SPARQL query logs. Proceedings of the VLDB Endowment (PVLDB), 11, 2017. Google Scholar
  9. Leizhen Cai and Junjie Ye. Finding two edge-disjoint paths with length constraints. In International Workshop on Graph-Theoretic Concepts in Computer Science (WG), pages 62-73, 2016. Google Scholar
  10. Mariano P. Consens and Alberto O. Mendelzon. GraphLog: a visual formalism for real life recursion. In Symposium on Principles of Database Systems (PODS), pages 404-416, 1990. Google Scholar
  11. Isabel F. Cruz, Alberto O. Mendelzon, and Peter T. Wood. A graphical query language supporting recursion. In ACM SIGMOD International Conference on Management of Data (SIGMOD), pages 323-330, 1987. Google Scholar
  12. Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Daniel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. Google Scholar
  13. Holger Dell. Personal communication, 2017. Google Scholar
  14. Rodney G. Downey and Michael R. Fellows. Fixed-parameter tractability and completeness I: basic results. SIAM Journal on Computing, 24(4):873-921, 1995. Google Scholar
  15. Rodney G. Downey and Michael R. Fellows. Fixed-parameter tractability and completeness II: on completeness for W[1]. Theoretical Computer Science (TCS), 141(1):109-131, 1995. Google Scholar
  16. Fedor V. Fomin, Daniel Lokshtanov, Fahad Panolan, and Saket Saurabh. Efficient computation of representative families with applications in parameterized and exact algorithms. Journal of the ACM, 63(4):29:1-29:60, 2016. Google Scholar
  17. Steven Fortune, John Hopcroft, and James Wyllie. The directed subgraph homeomorphism problem. Theoretical Computer Science (TCS), 10(2):111-121, 1980. Google Scholar
  18. Konstantin Golenberg, Benny Kimelfeld, and Yehoshua Sagiv. Optimizing and parallelizing ranked enumeration. Proceedings of the VLDB Endowment (PVLDB), 4(11):1028-1039, 2011. Google Scholar
  19. Martin Grohe and Magdalena Grüber. Parameterized approximability of the disjoint cycle problem. In International Colloquium on Automata, Languages and Programming (ICALP), pages 363-374, 2007. Google Scholar
  20. Oren Kalinsky, Yoav Etsion, and Benny Kimelfeld. Flexible caching in trie joins. In International Conference on Extending Database Technology (EDBT), pages 282-293, 2017. Google Scholar
  21. Sampath Kannan, Z. Sweedyk, and Stephen R. Mahaney. Counting and random generation of strings in regular languages. In Symposium on Discrete Algorithms (SODA), pages 551-557, 1995. Google Scholar
  22. Benny Kimelfeld and Yehoshua Sagiv. Extracting minimum-weight tree patterns from a schema with neighborhood constraints. In International Conference on Database Theory (ICDT), pages 249-260, 2013. Google Scholar
  23. Andrea S. LaPaugh and Christos H. Papadimitriou. The even-path problem for graphs and digraphs. Networks, 14(4):507-513, 1984. Google Scholar
  24. Eugene L. Lawler. A procedure for computing the k best solutions to discrete optimization problems and its application to the shortest path problem. Management Science, 18(7):401-405, 1972. Google Scholar
  25. Leonid Libkin, Wim Martens, and Domagoj Vrgoč. Querying graphs with data. Journal of the ACM, 63(2):14:1-14:53, 2016. Google Scholar
  26. Katja Losemann and Wim Martens. The complexity of regular expressions and property paths in SPARQL. ACM Transactions on Database Systems, 38(4):24:1-24:39, 2013. Google Scholar
  27. Erkki Mäkinen. On lexicographic enumeration of regular and context-free languages. Acta Cybernetica, 13(1):55-62, 1997. Google Scholar
  28. Wim Martens and Tina Trautner. Enumeration problems for regular path queries. CoRR, abs/1710.02317, 2017. URL: https://arxiv.org/abs/1710.02317.
  29. Alberto O. Mendelzon and Peter T. Wood. Finding regular simple paths in graph databases. SIAM Journal on Computing, 24(6):1235-1258, 12 1995. Google Scholar
  30. Katta G. Murty. An algorithm for ranking all the assignments in order of increasing cost. Operations Research, 16(3):682-687, 1968. Google Scholar
  31. Neo4j. Intro to cypher. https://neo4j.com/developer/cypher-query-language/, 2017.
  32. Neo4j. The neo4j developer manual v3.3. https://neo4j.com/docs/developer-manual/3.3/, 2017.
  33. Opencypher. https://www.opencypher.org. Visited on Sept. 14, 2017.
  34. Stefan Plantikow, Mats Rydberg, and Petra Selmer. CIP2017-01-18 - configurable pattern matching semantics. https://github.com/boggle/openCypher/blob/isomatch/cip/1.accepted/CIP2017-01-18-configurable-pattern-matching-semantics.adoc. Visited on Aug. 08, 2017.
  35. Aleksandrs Slivkins. Parameterized tractability of edge-disjoint paths on directed acyclic graphs. SIAM Journal on Discrete Mathematics, 24(1):146-157, 2010. Google Scholar
  36. Dimitri Surinx, George H. L. Fletcher, Marc Gyssens, Dirk Leinders, Jan Van den Bussche, Dirk Van Gucht, Stijn Vansummeren, and Yuqing Wu. Relative expressive power of navigational querying on graphs using transitive closure. Logic Journal of the IGPL, 23(5):759-788, 2015. Google Scholar
  37. Leslie G. Valiant. The complexity of computing the permanent. Theoretical Computer Science (TCS), 8(2):189-201, 1979. Google Scholar
  38. SPARQL 1.1 query language. https://www.w3.org/TR/sparql11-query/, 2013. World Wide Web Consortium.
  39. World wide web consortium. https://www.w3.org. Visited on Sept. 14, 2017.
  40. Mihalis Yannakakis. Graph-theoretic methods in database theory. In Symposium on Principles of Database Systems (PODS), pages 230-242, 1990. Google Scholar
  41. Jin Y. Yen. Finding the k shortest loopless paths in a network. Management Science, 17(11):712-716, 1971. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact