research-article

Dichotomies for Evaluating Simple Regular Path Queries

Authors:

Tina TrautnerAuthors Info & Claims

ACM Transactions on Database Systems (TODS), Volume 44, Issue 4

Article No.: 16, Pages 1 - 46

https://doi.org/10.1145/3331446

Published: 15 October 2019 Publication History

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, paths without node repetitions (simple paths), and paths without edge repetitions (trails).

Whereas arbitrary and shortest paths can be dealt with efficiently, simple paths and trails become computationally difficult already for very small RPQs. We study RPQ evaluation for simple paths and trails from a parameterized complexity perspective and define a class of simple transitive expressions that is prominent in practice and for which we can prove dichotomies for the evaluation problem. We observe that, even though simple path and trail semantics are intractable for RPQs in general, they are feasible for the vast majority of RPQs that are used in practice. At the heart of this study 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.

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References

[1]

Margareta Ackerman and Jeffrey Shallit. 2009. Efficient enumeration of words in regular languages. Theoretical Computer Science (TCS) 410, 37 (2009), 3461--3470.

Digital Library

[2]

Noga Alon, Raphael Yuster, and Uri Zwick. 1995. Color-coding. Journal of the ACM 42, 4 (1995), 844--856.

Digital Library

[3]

Renzo Angles, Marcelo Arenas, Pablo Barceló, Peter A. Boncz, George H. L. Fletcher, Claudio Gutierrez, Tobias Lindaaker, Marcus Paradies, Stefan Plantikow, Juan F. Sequeda, Oskar van Rest, and Hannes Voigt. 2018. G-CORE: A core for future graph query languages. In International Conference on Management of Data (SIGMOD). 1421--1432.

Digital Library

[4]

Renzo Angles, Marcelo Arenas, Pablo Barceló, Aidan Hogan, Juan L. Reutter, and Domagoj Vrgoč. 2017. Foundations of modern query languages for graph databases. Comput. Surveys 50, 5 (2017), 68:1--68:40.

[5]

Marcelo Arenas, Sebastián Conca, and Jorge Pérez. 2012. 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). 629--638.

Digital Library

[6]

Guillaume Bagan, Angela Bonifati, and Benoît Groz. 2012. A trichotomy for regular simple path queries on graphs. CoRR abs/1212.6857 (2012). http://arxiv.org/abs/1212.6857.

[7]

Guillaume Bagan, Angela Bonifati, and Benoît Groz. 2013. A trichotomy for regular simple path queries on graphs. In Symposium on Principles of Database Systems (PODS). 261--272.

Digital Library

[8]

Pablo Barceló. 2013. Querying graph databases. In Symposium on Principles of Database Systems (PODS). 175--188.

[9]

Geert Jan Bex, Wim Martens, Frank Neven, and Thomas Schwentick. 2005. Expressiveness of XSDs: From practice to theory, there and back again. In International Conference on World Wide Web (WWW). 712--721.

Digital Library

[10]

Geert Jan Bex, Frank Neven, and Jan Van den Bussche. 2004. DTDs versus XML schema: A practical study. In Proceedings of the 7th International Workshop on the Web and Databases (WebDB). 79--84.

Digital Library

[11]

Geert Jan Bex, Frank Neven, Thomas Schwentick, and Stijn Vansummeren. 2010. Inference of concise regular expressions and DTDs. ACM Transactions on Database Systems 35, 2 (2010), 11:1--11:47.

Digital Library

[12]

Geert Jan Bex, Frank Neven, and Stijn Vansummeren. 2007. Inferring XML schema definitions from XML data (VLDB). In International Conference on Very Large Data Bases. 998--1009.

[13]

Andreas Björklund, Thore Husfeldt, and Sanjeev Khanna. 2004. Approximating longest directed paths and cycles. In International Colloquium on Automata, Languages and Programming (ICALP). 222--233.

[14]

Angela Bonifati, Wim Martens, and Thomas Tim. 2019. Navigating the maze of wikidata query logs. In The Web Conference (WWW). ACM. To appear.

Digital Library

[15]

Angela Bonifati, Wim Martens, and Thomas Timm. 2017. An analytical study of large SPARQL query logs. Proceedings of the VLDB Endowment (PVLDB) 11, 2 (2017), 149--161.

Digital Library

[16]

Janusz A. Brzozowski. 1964. Derivatives of regular expressions. Journal of the ACM 11, 4 (Oct. 1964), 481--494.

Digital Library

[17]

Leizhen Cai and Junjie Ye. 2016. Finding two edge-disjoint paths with length constraints. In International Workshop on Graph-Theoretic Concepts in Computer Science (WG). 62–73.

Digital Library

[18]

Yijia Chen and Jörg Flum. 2007. On parameterized path and chordless path problems. In IEEE Conference on Computational Complexity (CCC). 250--263.

Digital Library

[19]

Mariano P. Consens and Alberto O. Mendelzon. 1990. GraphLog: A visual formalism for real life recursion. In Symposium on Principles of Database Systems (PODS). 404--416.

[20]

Isabel F. Cruz, Alberto O. Mendelzon, and Peter T. Wood. 1987. A graphical query language supporting recursion. In ACM SIGMOD International Conference on Management of Data (SIGMOD). 323--330.

[21]

Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Daniel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. 2015. Parameterized Algorithms. Springer.

[22]

Holger Dell. 2017. Personal communication.

[23]

Rodney G. Downey and Michael R. Fellows. 1995. Fixed-parameter tractability and completeness I: Basic results. SIAM J. Comput. 24, 4 (1995), 873--921.

Digital Library

[24]

Rodney G. Downey and Michael R. Fellows. 1995. Fixed-parameter tractability and completeness II: On completeness for W[1]. Theoretical Computer Science (TCS) 141, 1 (1995), 109--131.

Digital Library

[25]

Jörg Flum and Martin Grohe. 2004. The parameterized complexity of counting problems. SIAM J. Comput. 33, 4 (2004), 892--922.

Digital Library

[26]

Fedor V. Fomin, Daniel Lokshtanov, Fahad Panolan, and Saket Saurabh. 2016. Efficient computation of representative families with applications in parameterized and exact algorithms. Journal of the ACM 63, 4 (2016), 29:1--29:60.

Digital Library

[27]

Steven Fortune, John Hopcroft, and James Wyllie. 1980. The directed subgraph homeomorphism problem. Theoretical Computer Science (TCS) 10, 2 (1980), 111--121.

[28]

Konstantin Golenberg, Benny Kimelfeld, and Yehoshua Sagiv. 2011. Optimizing and parallelizing ranked enumeration. Proceedings of the VLDB Endowment (PVLDB) 4, 11 (2011), 1028--1039.

Digital Library

[29]

Martin Grohe and Magdalena Grüber. 2007. Parameterized approximability of the disjoint cycle problem. In International Colloquium on Automata, Languages and Programming (ICALP). 363--374.

[30]

Oren Kalinsky, Yoav Etsion, and Benny Kimelfeld. 2017. Flexible caching in trie joins. In International Conference on Extending Database Technology (EDBT). 282--293.

[31]

Sampath Kannan, Z. Sweedyk, and Stephen R. Mahaney. 1995. Counting and random generation of strings in regular languages. In Symposium on Discrete Algorithms (SODA). 551--557.

[32]

Benny Kimelfeld and Yehoshua Sagiv. 2013. Extracting minimum-weight tree patterns from a schema with neighborhood constraints. In International Conference on Database Theory (ICDT). 249--260.

Digital Library

[33]

Andrea S. LaPaugh and Christos H. Papadimitriou. 1984. The even-path problem for graphs and digraphs. Networks 14, 4 (1984), 507--513.

[34]

Andrea S. LaPaugh and Ronald L. Rivest. 1980. The subgraph homeomorphism problem. J. Comput. System Sci. 20, 2 (1980), 133--149.

[35]

Eugene L. Lawler. 1972. A procedure for computing the K best solutions to discrete optimization problems and its application to the shortest path problem. Management Science 18, 7 (1972), 401--405.

Digital Library

[36]

Leonid Libkin, Wim Martens, and Domagoj Vrgoč. 2016. Querying graphs with data. Journal of the ACM 63, 2 (2016), 14:1--14:53.

Digital Library

[37]

Katja Losemann and Wim Martens. 2013. The complexity of regular expressions and property paths in SPARQL. ACM Transactions on Database Systems 38, 4 (2013), 24:1--24:39.

Digital Library

[38]

Erkki Mäkinen. 1997. On lexicographic enumeration of regular and context-free languages. Acta Cybernetica 13, 1 (1997), 55--62.

Digital Library

[39]

Wim Martens, Frank Neven, Matthias Niewerth, and Thomas Schwentick. 2017. BonXai: Combining the simplicity of DTD with the expressiveness of XML schema. ACM Transactions on Database Systems 42, 3 (2017), 15:1--15:42.

Digital Library

[40]

Wim Martens, Frank Neven, and Thomas Schwentick. 2004. Complexity of decision problems for simple regular expressions. In Mathematical Foundations of Computer Science (MFCS). 889--900.

[41]

Wim Martens and Tina Trautner. 2018. Evaluation and enumeration problems for regular path queries. In International Conference on Database Theory (ICDT). 19:1--19:21.

[42]

Alberto O. Mendelzon and Peter T. Wood. 1995. Finding regular simple paths in graph databases. SIAM J. Comput. 24, 6 (1995), 1235--1258.

Digital Library

[43]

B. Monien. 1985. How to find long paths efficiently. In Analysis and Design of Algorithms for Combinatorial Problems. North-Holland Mathematics Studies, Vol. 109. North-Holland, 239--254.

[44]

Katta G. Murty. 1968. An algorithm for ranking all the assignments in order of increasing cost. Operations Research 16, 3 (1968), 682--687.

Digital Library

[45]

Neo4j. 2017. Intro to Cypher. https://neo4j.com/developer/cypher-query-language/.

[46]

OpenCypher [n.d.]. OpenCypher. www.opencypher.org. Visited on Sept. 14, 2017.

[47]

Yehoshua Perl and Yossi Shiloach. 1978. Finding two disjoint paths between two pairs of vertices in a graph. Journal of the ACM 25, 1 (1978), 1--9.

Digital Library

[48]

Stefan Plantikow, Mats Rydberg, and Petra Selmer. [n.d.]. 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.

[49]

Steven Skiena. 2008. The Algorithm Design Manual (2nd ed.). Springer.

Digital Library

[50]

Aleksandrs Slivkins. 2010. Parameterized tractability of edge-disjoint paths on directed acyclic graphs. SIAM Journal on Discrete Mathematics 24, 1 (2010), 146--157.

Digital Library

[51]

Dimitri Surinx, George H. L. Fletcher, Marc Gyssens, Dirk Leinders, Jan Van den Bussche, Dirk Van Gucht, Stijn Vansummeren, and Yuqing Wu. 2015. Relative expressive power of navigational querying on graphs using transitive closure. Logic Journal of the IGPL 23, 5 (2015), 759--788.

[52]

Leslie G. Valiant. 1979. The complexity of enumeration and reliability problems. SIAM J. Comput. 8, 3 (1979), 410--421.

Digital Library

[53]

Domagoj Vrgoč. 2018. Personal communication. After a talk of Wim Martens at PUC Chile, the query was discussed in more detail and Domagoj Vrgoč, who attended the talk, informed us that he wrote the query.

[54]

W3C SPARQL 2013. SPARQL 1.1 Query Language. https://www.w3.org/TR/sparql11-query/. World Wide Web Consortium.

[55]

World Wide Web Consortium [n.d.]. World Wide Web Consortium. www.w3.org. Visited on Sept. 14, 2017.

[56]

Mihalis Yannakakis. 1990. Graph-theoretic methods in database theory. In Symposium on Principles of Database Systems (PODS). 230--242.

Digital Library

[57]

Jin Y. Yen. 1971. Finding the K shortest loopless paths in a network. Management Science 17, 11 (1971), 712--716.

Digital Library

[58]

Jin Y. Yen. 1972. Finding the lengths of all shortest paths in N-node nonnegative-distance complete networks using ½N³ additions and N³ comparisons. Journal of the ACM 19, 3 (1972), 423--424.

Digital Library

Cited By

García RAngles R(2024)Path Querying in Graph Databases: A Systematic Mapping StudyIEEE Access10.1109/ACCESS.2024.337197612(33154-33172)Online publication date: 2024
https://doi.org/10.1109/ACCESS.2024.3371976
Martens WNiewerth MPopp TRojas CVansummeren SVrgoč D(2023)Representing Paths in Graph Database Pattern MatchingProceedings of the VLDB Endowment10.14778/3587136.358715116:7(1790-1803)Online publication date: 8-May-2023
https://dl.acm.org/doi/10.14778/3587136.3587151
Figueira DRomero MGeerts FNgo HSintos S(2023)Conjunctive Regular Path Queries under Injective SemanticsProceedings of the 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3584372.3588664(231-240)Online publication date: 18-Jun-2023
https://dl.acm.org/doi/10.1145/3584372.3588664
Show More Cited By

Index Terms

Dichotomies for Evaluating Simple Regular Path Queries
1. Information systems
  1. Data management systems
    1. Query languages
      1. Query languages for non-relational engines
2. Theory of computation
  1. Formal languages and automata theory
    1. Regular languages
  2. Theory and algorithms for application domains
    1. Database theory
      1. Database query languages (principles)

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cover image ACM Transactions on Database Systems

ACM Transactions on Database Systems Volume 44, Issue 4

Best of EDBT 2017, Best of EDBT 2018, Best of ICDT 2018 and Regular Papers

December 2019

249 pages

ISSN:0362-5915

EISSN:1557-4644

DOI:10.1145/3366712

Editor:
Christian S. Jensen
Aalborg University, Denmark

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Copyright © 2019 ACM.

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Publication History

Published: 15 October 2019

Accepted: 01 May 2019

Revised: 01 March 2019

Received: 01 August 2018

Published in TODS Volume 44, Issue 4

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Cited By

García RAngles R(2024)Path Querying in Graph Databases: A Systematic Mapping StudyIEEE Access10.1109/ACCESS.2024.337197612(33154-33172)Online publication date: 2024
https://doi.org/10.1109/ACCESS.2024.3371976
Martens WNiewerth MPopp TRojas CVansummeren SVrgoč D(2023)Representing Paths in Graph Database Pattern MatchingProceedings of the VLDB Endowment10.14778/3587136.358715116:7(1790-1803)Online publication date: 8-May-2023
https://dl.acm.org/doi/10.14778/3587136.3587151
Figueira DRomero MGeerts FNgo HSintos S(2023)Conjunctive Regular Path Queries under Injective SemanticsProceedings of the 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3584372.3588664(231-240)Online publication date: 18-Jun-2023
https://dl.acm.org/doi/10.1145/3584372.3588664
Martens WLibkin LBarceló P(2022)Towards Theory for Real-World DataProceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3517804.3526066(261-276)Online publication date: 12-Jun-2022
https://dl.acm.org/doi/10.1145/3517804.3526066
Martens WPopp TLibkin LBarceló P(2022)The Complexity of Regular Trail and Simple Path Queries on Undirected GraphsProceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3517804.3524149(165-174)Online publication date: 12-Jun-2022
https://dl.acm.org/doi/10.1145/3517804.3524149
Schmid M(2022)Conjunctive Regular Path Queries with Capture GroupsACM Transactions on Database Systems10.1145/351423047:2(1-52)Online publication date: 23-May-2022
https://dl.acm.org/doi/10.1145/3514230
Angles RBonifati ADumbrava SFletcher GHare KHidders JLee VLi BLibkin LMartens WMurlak FPerryman JSavković OSchmidt MSequeda JStaworko STomaszuk DLi GLi ZIdreos SSrivastava D(2021)PG-Keys: Keys for Property GraphsProceedings of the 2021 International Conference on Management of Data10.1145/3448016.3457561(2423-2436)Online publication date: 9-Jun-2021
https://dl.acm.org/doi/10.1145/3448016.3457561
Arenas MGutierrez CSequeda JLi GLi ZIdreos SSrivastava D(2021)Querying in the Age of Graph Databases and Knowledge GraphsProceedings of the 2021 International Conference on Management of Data10.1145/3448016.3457545(2821-2828)Online publication date: 9-Jun-2021
https://dl.acm.org/doi/10.1145/3448016.3457545
Arenas MCroquevielle LJayaram RRiveros C(2020)Efficient Logspace Classes for Enumeration, Counting, and Uniform GenerationACM SIGMOD Record10.1145/3422648.342266149:1(52-59)Online publication date: 4-Sep-2020
https://dl.acm.org/doi/10.1145/3422648.3422661
Martens W(2020)Formal Languages in Information Extraction and Graph DatabasesBeyond the Horizon of Computability10.1007/978-3-030-51466-2_28(306-309)Online publication date: 29-Jun-2020
https://dl.acm.org/doi/10.1007/978-3-030-51466-2_28
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