research-article

A trichotomy for regular simple path queries on graphs

Authors:

Guillaume Bagan,

Angela Bonifati,

Benoit GrozAuthors Info & Claims

PODS '13: Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI symposium on Principles of database systems

Pages 261 - 272

https://doi.org/10.1145/2463664.2467795

Published: 22 June 2013 Publication History

Abstract

Regular path queries (RPQs) select vertices connected by some path in a graph. The edge labels of such a path have to form a word that matches a given regular expression. We investigate the evaluation of RPQs with an additional constraint that prevents multiple traversals of the same vertices. Those regular simple path queries (RSPQs) quickly become intractable, even for basic languages such as (aa)* or a*ba*.

In this paper, we establish a comprehensive classification of regular languages with respect to the complexity of the corresponding regular simple path query problem. More precisely, we identify for which languages RSPQs can be evaluated in polynomial time, and show that evaluation is NP-complete for languages outside this fragment. We thus fully characterize the frontier between tractability and intractability for RSPQs, and we refine our results to show the following trichotomy: evaluation of RSPQs is either AC0, NL-complete or NP-complete in data complexity, depending on the language L. The fragment identified also admits a simple characterization in terms of regular expressions.

Finally, we also discuss the complexity of deciding whether a language L belongs to the fragment above. We consider several alternative representations of L: DFAs, NFAs or regular expressions, and prove that this problem is NL-complete for the first representation and PSPACE-complete for the other two. As a conclusion we extend our results from edge-labeled graphs to vertex-labeled graphs.

References

[1]

S. Abiteboul and V. Vianu. Regular path queries with constraints. J. Comput. Syst. Sci., 58(3):428--452, 1999.

Digital Library

[2]

N. Alon, R. Yuster, and U. Zwick. Color-Coding. J. ACM, 42(4):844--856, 1995.

Digital Library

[3]

M. Arenas, S. Conca, and J. Pérez. Counting beyond a yottabyte, or how sparql 1.1 property paths will prevent adoption of the standard. In WWW, pages 629--638, 2012.

Digital Library

[4]

E. M. Arkin, C. H. Papadimitriou, and M. Yannakakis. Modularity of Cycles and Paths in Graphs. J. ACM, 38(2):255--274, 1991.

Digital Library

[5]

G. Bagan, A. Bonifati, and B. Groz. A trichotomy for regular simple path queries on graphs. CoRR, abs/1212.6857, 2012.

[6]

P. Barceló, L. Libkin, and J. L. Reutter. Querying graph patterns. In PODS, pages 199--210. ACM, 2011.

Digital Library

[7]

C. L. Barrett, R. Jacob, and M. V. Marathe. Formal-language-constrained path problems. SIAM Journal on Computing, 30(3):809--837, 2000.

Digital Library

[8]

D. Berwanger, A. Dawar, P. Hunter, S. Kreutzer, and J. Obdrzálek. The dag-width of directed graphs. J. Comb. Theory, Ser. B, 102(4):900--923, 2012.

Digital Library

[9]

D. Calvanese, G. D. Giacomo, M. Lenzerini, and M. Y. Vardi. Answering regular path queries using views. In ICDE, pages 389--398, 2000.

Digital Library

[10]

D. Calvanese, G. D. Giacomo, M. Lenzerini, and M. Y. Vardi. Rewriting of regular expressions and regular path queries. J. Comput. Syst. Sci., 64(3):443--465, 2002.

Digital Library

[11]

D. Calvanese, G. D. Giacomo, M. Lenzerini, and M. Y. Vardi. Reasoning on regular path queries. SIGMOD Record, 32(4):83--92, 2003.

Digital Library

[12]

D. Calvanese, G. D. Giacomo, M. Lenzerini, and M. Y. Vardi. An automata-theoretic approach to regular xpath. In DBPL, pages 18--35, 2009.

Digital Library

[13]

B. Courcelle. Graph rewriting: An algebraic and logic approach. In Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics (B), pages 193--242. 1990.

Digital Library

[14]

I. F. Cruz, A. O. Mendelzon, and P. T. Wood. A graphical query language supporting recursion. In SIGMOD Conference, pages 323--330, 1987.

Digital Library

[15]

W. Fan, J. Li, S. Ma, N. Tang, and Y. Wu. Adding regular expressions to graph reachability and pattern queries. In ICDE, pages 39--50. IEEE Computer Society, 2011.

Digital Library

[16]

J. Flum and M. Grohe. Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series). 2006.

Digital Library

[17]

M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979.

Digital Library

[18]

C. Gutierrez, C. A. Hurtado, A. O. Mendelzon, and J. Pérez. Foundations of semantic web databases. J. Comput. Syst. Sci., 77(3):520--541, 2011.

Digital Library

[19]

R. H. Gäting. GraphDB: A Data Model and Query Language for Graphs in Databases. In Proc. 20th Int. Conf. on Very Large Data Bases, pages 297--308, 1994.

Digital Library

[20]

P. Hunter and S. Kreutzer. Digraph measures: Kelly decompositions, games, and orderings. Theor. Comput. Sci., 399(3):206--219, 2008.

Digital Library

[21]

N. Immerman. Nondeterministic space is closed under complementation. SIAM J. Comput., 17(5):935--938, 1988.

Digital Library

[22]

N. Immerman. Descriptive complexity. Springer, 1999.

[23]

R. Jin, H. Hong, H. Wang, N. Ruan, and Y. Xiang. Computing label-constraint reachability in graph databases. In SIGMOD Conference, pages 123--134, 2010.

Digital Library

[24]

T. Johnson, N. Robertson, P. D. Seymour, and R. Thomas. Directed tree-width. J. Comb. Theory, Ser. B, 82(1):138--154, 2001.

Digital Library

[25]

A. Koschmieder and U. Leser. Regular path queries on large graphs. In SSDBM, pages 177--194, 2012.

Digital Library

[26]

A. S. Lapaugh and C. H. Papadimitriou. The even-path problem for graphs and digraphs. Networks}, 14(4):507--513, 1984.

[27]

U. Leser. A query language for biological networks. In ECCB/JBI, page 39, 2005.

[28]

L. Libkin and D. Vrgoc. Regular Path Queries on Graphs with Data. In ICDT 2012, pages 74--85, 2012.

Digital Library

[29]

K. Losemann and W. Martens. The complexity of evaluating path expressions in sparql. In PODS, pages 101--112. ACM, 2012.

Digital Library

[30]

A. O. Mendelzon and P. T. Wood. Finding Regular Simple Paths in Graph Databases. SIAM J. Comput., 24(6):1235--1258, 1995.

Digital Library

[31]

Z. P. Nedev. Finding an Even Simple Path in a Directed Planar Graph. SIAM J. Comput., 29:685--695, 1999.

Digital Library

[32]

Z. P. Nedev and P. T. Wood. A polynomial-time algorithm for finding regular simple paths in outerplanar graphs. J. Algorithms, 35(2):235--259, 2000.

Digital Library

[33]

F. Olken. Graph data management for molecular biology. OMICS, 7(1):75--78, 2003.

[34]

C. H. Papadimitriou. Computational complexity. Addison-Wesley, 1994.

[35]

N. Robertson and P. D. Seymour. Graph Minors .XIII. The Disjoint Paths Problem. J. Comb. Theory, Ser. B, 63(1):65--110, 1995.

Digital Library

[36]

R. Ronen and O. Shmueli. Soql: A language for querying and creating data in social networks. In ICDE, pages 1595--1602, 2009.

Digital Library

[37]

W. L. Ruzzo, J. Simon, and M. Tompa. Space-bounded hierarchies and probabilistic computations. J. Comput. Syst. Sci.}, 28(2):216--230, 1984.

[38]

A. Schrijver. Finding k Disjoint Paths in a Directed Planar Graph. SIAM J. Comput., 23(4):780--788, 1994.

Digital Library

[39]

M. P. Schützenberger. On finite monoids having only trivial subgroups. Information and Control, 8(2):190--194, 1965.

[40]

L. J. Stockmeyer and A. R. Meyer. Word problems requiring exponential time: Preliminary report. In STOC, pages 1--9, 1973.

Digital Library

[41]

C. B. Ward and N. M. Wiegand. Complexity results on labeled shortest path problems from wireless routing metrics. Computer Networks, 54(2):208--217, 2010.

Digital Library

Cited By

Hang JHong ZFeng XWang GCao DQiao JWang HZhang D(2024)Complex-Path: Effective and Efficient Node Ranking with Paths in Billion-Scale Heterogeneous GraphsProceedings of the VLDB Endowment10.14778/3685800.368582017:12(3973-3986)Online publication date: 8-Nov-2024
https://dl.acm.org/doi/10.14778/3685800.3685820
Liang QOuyang DZhang FYang JLin XTian Z(2024)Efficient Regular Simple Path Queries under Transitive Restricted ExpressionsProceedings of the VLDB Endowment10.14778/3654621.365463617:7(1710-1722)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.14778/3654621.3654636
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
Show More Cited By

Index Terms

A trichotomy for regular simple path queries on graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

PODS '13: Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI symposium on Principles of database systems

June 2013

334 pages

ISBN:9781450320665

DOI:10.1145/2463664

General Chair:
Richard Hull
IBM T.J. Watson Research Center, USA
,
Program Chair:
Wenfei Fan
University of Edinburgh, UK

Copyright © 2013 ACM.

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Published: 22 June 2013

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SIGMOD/PODS'13: International Conference on Management of Data

June 22 - 27, 2013

New York, New York, USA

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PODS '13 Paper Acceptance Rate 24 of 97 submissions, 25%;

Overall Acceptance Rate 642 of 2,707 submissions, 24%

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Cited By

Hang JHong ZFeng XWang GCao DQiao JWang HZhang D(2024)Complex-Path: Effective and Efficient Node Ranking with Paths in Billion-Scale Heterogeneous GraphsProceedings of the VLDB Endowment10.14778/3685800.368582017:12(3973-3986)Online publication date: 8-Nov-2024
https://dl.acm.org/doi/10.14778/3685800.3685820
Liang QOuyang DZhang FYang JLin XTian Z(2024)Efficient Regular Simple Path Queries under Transitive Restricted ExpressionsProceedings of the VLDB Endowment10.14778/3654621.365463617:7(1710-1722)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.14778/3654621.3654636
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
Wang HWang XMa MYou Y(2024)RPQBench: A Benchmark for Regular Path Queries on Graph DataWeb Information Systems Engineering – WISE 202410.1007/978-981-96-0567-5_25(351-367)Online publication date: 3-Dec-2024
https://doi.org/10.1007/978-981-96-0567-5_25
Farías BMartens WRojas CVrgoč D(2024)PathFinder: Returning Paths in Graph QueriesThe Semantic Web – ISWC 202410.1007/978-3-031-77850-6_8(135-154)Online publication date: 11-Nov-2024
https://dl.acm.org/doi/10.1007/978-3-031-77850-6_8
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
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Koutris PDeep S(2023)The Fine-Grained Complexity of CFL ReachabilityProceedings of the ACM on Programming Languages10.1145/35712527:POPL(1713-1739)Online publication date: 11-Jan-2023
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Zhang CBonifati AKapp HHaprian VLozi J(2023)A Reachability Index for Recursive Label-Concatenated Graph Queries2023 IEEE 39th International Conference on Data Engineering (ICDE)10.1109/ICDE55515.2023.00013(67-81)Online publication date: Apr-2023
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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
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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
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