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From relation algebra to semi-join algebra: an approach for graph query optimization

Authors:

Jelle Hellings,

Catherine L. Pilachowski,

Dirk Van Gucht,

Yuqing WuAuthors Info & Claims

DBPL '17: Proceedings of The 16th International Symposium on Database Programming Languages

Article No.: 5, Pages 1 - 10

https://doi.org/10.1145/3122831.3122833

Published: 01 September 2017 Publication History

Abstract

Many graph query languages rely on the composition operator to navigate graphs and select nodes of interests, even though evaluating compositions of relations can be costly. Often, this need for composition can be reduced by rewriting towards queries that use semi-joins instead. In this way, the cost of evaluating queries can be significantly reduced.

We study techniques to recognize and apply such rewritings. Concretely, we study the relationship between the expressive power of the relation algebras, that heavily rely on composition, and the semi-join algebras, that replace the composition operator in favor of the semi-join operators.

As our main result, we show that each fragment of the relation algebras where intersection and/or difference is only used on edges (and not on complex compositions) is expressively equivalent to a fragment of the semi-join algebras. This expressive equivalence holds for node queries that evaluate to sets of nodes. For practical relevance, we exhibit constructive steps for rewriting relation algebra queries to semi-join algebra queries, and prove that these steps lead to only a well-bounded increase in the number of steps needed to evaluate the rewritten queries.

In addition, on node-labeled graphs that are sibling-ordered trees, we establish new relationships among the expressive power of Regular XPath, Conditional XPath, FO-logic, and the semi-join algebra augmented with restricted fixpoint operators.

References

[1]

Pablo Barceló. 2013. Querying Graph Databases. In Proceedings of the 32nd Symposium on Principles of Database Systems (PODS '13). ACM, 175--188.

Digital Library

[2]

Michael Benedikt, Wenfei Fan, and Gabriel Kuper. 2005. Structural properties of XPath fragments. Theoretical Computer Science 336, 1 (2005), 3--31.

Digital Library

[3]

Michael Benedikt and Christoph Koch. 2009. XPath Leashed. ACM Computing Surveys (CSUR) 41, 1 (2009), 3:1--3:54.

[4]

Philip A. Bernstein and Dah-Ming W. Chiu. 1981. Using Semi-Joins to Solve Relational Queries. J. ACM 28, 1 (1981), 25--40.

Digital Library

[5]

James Clark and Steve DeRose. 1999. XML Path Language (XPath) Version 1.0. W3C Recommendation. W3C. http://www.w3.org/TR/1999/REC-xpath-19991116.

[6]

Rance Cleaveland and Bernhard Steffen. 1993. A linear-time model-checking algorithm for the alternation-free modal mu-calculus. Formal Methods in System Design 2, 2 (1993), 121--147.

Digital Library

[7]

George H. L. Fletcher, Marc Gyssens, Dirk Leinders, Dimitri Surinx, Jan Van den Bussche, Dirk Van Gucht, Stijn Vansummeren, and Yuqing Wu. 2015. Relative expressive power of navigational querying on graphs. Information Sciences 298 (2015), 390--406.

Digital Library

[8]

George H. L. Fletcher, Marc Gyssens, Dirk Leinders, Jan Van den Bussche, Dirk Van Gucht, Stijn Vansummeren, and Yuqing Wu. 2015. The impact of transitive closure on the expressiveness of navigational query languages on unlabeled graphs. Annals of Mathematics and Artificial Intelligence 73, 1--2 (2015), 167--203.

Digital Library

[9]

Hector Garcia-Molina, Jeffrey D. Ullman, and Jennifer Widom. 2008. Database Systems: The Complete Book (2 ed.). Prentice Hall Press, Upper Saddle River, NJ, USA.

Digital Library

[10]

Steven Givant. 2006. The Calculus of Relations as a Foundation for Mathematics. Journal of Automated Reasoning 37, 4 (2006), 277--322.

Digital Library

[11]

Martin Grohe. 1998. Finite Variable Logics in Descriptive Complexity Theory. The Bulletin of Symbolic Logic 4 (1998), 345--398.

[12]

Jelle Hellings, Marc Gyssens, Yuqing Wu, Dirk Van Gucht, Jan Van den Bussche, Stijn Vansummeren, and George H. L. Fletcher. 2015. Relative Expressive Power of Downward Fragments of Navigational Query Languages on Trees and Chains. In Proceedings of the 15th Symposium on Database Programming Languages (DBPL 2015). 59--68.

Digital Library

[13]

Aviel Klausner and Nathan Goodman. 1985. Multirelations: Semantice and Languages. In Proceedings of the 11th International Conference on Very Large Data Bases (VLDB '85). VLDB Endowment, 251--258.

[14]

Dexter Kozen. 1997. Kleene Algebra with Tests. ACM Transactions on Programming Languages and Systems 19, 3 (1997), 427--443.

Digital Library

[15]

Dirk Leinders. 2008. The semijoin algebra. Ph.D. Dissertation. Hasselt University and transnational University of Limburg.

[16]

Dirk Leinders, Maarten Marx, Jerzy Tyszkiewicz, and Jan Van den Bussche. 2005. The Semijoin Algebra and the Guarded Fragment. Journal of Logic, Language and Information 14, 3 (2005), 331--343.

Digital Library

[17]

Dirk Leinders, Jerzy Tyszkiewicz, and Jan Van den Bussche. 2004. On the expressive power of semijoin queries. Inform. Process. Lett. 91, 2 (2004), 93--98.

Digital Library

[18]

Dirk Leinders and Jan Van den Bussche. 2007. On the complexity of division and set joins in the relational algebra. J. Comput. System Sci. 73, 4 (2007), 538--549. Special Issue: Database Theory 2005.

Digital Library

[19]

Leonid Libkin, Wim Martens, and Domagoj Vrgoč. 2013. Querying Graph Databases with XPath. In Proceedings of the 16th International Conference on Database Theory (ICDT '13). ACM, New York, NY, USA, 129--140.

Digital Library

[20]

Maarten Marx. 2005. Conditional XPath. ACM Transactions on Database Systems 30, 4 (2005), 929--959.

Digital Library

[21]

Maarten Marx and Maarten de Rijke. 2005. Semantic Characterizations of Navigational XPath. SIGMOD Record 34, 2 (2005), 41--46.

Digital Library

[22]

Maarten Marx and Yde Venema. 1997. Multi-Dimensional Modal Logic. Springer Netherlands, Dordrecht.

[23]

Praveen Seshadri, Joseph M. Hellerstein, Hamid Pirahesh, T. Y. Cliff Leung, Raghu Ramakrishnan, Divesh Srivastava, Peter J. Stuckey, and S. Sudarshan. 1996. Cost-based Optimization for Magic: Algebra and Implementation. SIGMOD Rec. 25, 2 (1996), 435--446.

Digital Library

[24]

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.

[25]

Alfred Tarski. 1941. On the Calculus of Relations. The Journal of Symbolic Logic 6, 3 (1941), 73--89.

[26]

Balder ten Cate. 2006. The Expressivity of XPath with Transitive Closure. In Proceedings of the Twenty-fifth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS '06). ACM, 328--337.

Digital Library

[27]

Balder ten Cate and Maarten Marx. 2007. Navigational XPath: Calculus and Algebra. SIGMOD Record 36, 2 (2007), 19--26.

Digital Library

[28]

Jeffrey D. Ullman. 1990. Principles of Database and Knowledge-Base Systems: Volume II: The New Technologies. W. H. Freeman & Co., New York, NY, USA.

[29]

Moshe Y. Vardi. 1982. The Complexity of Relational Query Languages (Extended Abstract). In Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing (STOC '82). ACM, New York, NY, USA, 137--146.

Digital Library

[30]

Yuqing Wu, Dirk Van Gucht, Marc Gyssens, and Jan Paredaens. 2011. A Study of a Positive Fragment of Path Queries: Expressiveness, Normal Form and Minimization. Comput. J. 54, 7 (2011), 1091--1118.

Digital Library

[31]

Mihalis Yannakakis. 1981. Algorithms for Acyclic Database Schemes. In Proceedings of the Seventh International Conference on Very Large Data Bases - Volume 7 (VLDB '81). VLDB Endowment, 82--94.

Cited By

Hellings JWu YGyssens MVan Gucht D(2022)The power of Tarski's relation algebra on treesJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2022.100748(100748)Online publication date: Jan-2022
https://doi.org/10.1016/j.jlamp.2022.100748
Hellings JWu YVan Gucht DGyssens M(2022)Optimizing Multiset Relational Algebra Queries Using Weak-Equivalent Rewrite RulesFoundations of Information and Knowledge Systems10.1007/978-3-031-11321-5_11(187-205)Online publication date: 10-Jul-2022
https://doi.org/10.1007/978-3-031-11321-5_11
Hellings JPilachowski CVan Gucht DGyssens MWu Y(2020)From Relation Algebra to Semi-join Algebra: An Approach to Graph Query OptimizationThe Computer Journal10.1093/comjnl/bxaa031Online publication date: 9-May-2020
https://doi.org/10.1093/comjnl/bxaa031
Show More Cited By

Index Terms

From relation algebra to semi-join algebra: an approach for graph query optimization
1. Theory of computation
  1. Logic
    1. Finite Model Theory
  2. Theory and algorithms for application domains
    1. Database theory

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cover image ACM Other conferences

DBPL '17: Proceedings of The 16th International Symposium on Database Programming Languages

September 2017

99 pages

ISBN:9781450353540

DOI:10.1145/3122831

Conference Chairs:
Tiark Rompf
Purdue University
,
Alexander Alexandrov
TU Berlin, Germany

Copyright © 2017 ACM.

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Published: 01 September 2017

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DBPL 2017: The 16th International Symposium on Database Programming Languages

September 1, 2017

Munich, Germany

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DBPL '17 Paper Acceptance Rate 10 of 15 submissions, 67%;

Overall Acceptance Rate 10 of 15 submissions, 67%

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Cited By

Hellings JWu YGyssens MVan Gucht D(2022)The power of Tarski's relation algebra on treesJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2022.100748(100748)Online publication date: Jan-2022
https://doi.org/10.1016/j.jlamp.2022.100748
Hellings JWu YVan Gucht DGyssens M(2022)Optimizing Multiset Relational Algebra Queries Using Weak-Equivalent Rewrite RulesFoundations of Information and Knowledge Systems10.1007/978-3-031-11321-5_11(187-205)Online publication date: 10-Jul-2022
https://doi.org/10.1007/978-3-031-11321-5_11
Hellings JPilachowski CVan Gucht DGyssens MWu Y(2020)From Relation Algebra to Semi-join Algebra: An Approach to Graph Query OptimizationThe Computer Journal10.1093/comjnl/bxaa031Online publication date: 9-May-2020
https://doi.org/10.1093/comjnl/bxaa031
Hellings JWu YGyssens MVan Gucht D(2018)The Power of Tarski’s Relation Algebra on TreesFoundations of Information and Knowledge Systems10.1007/978-3-319-90050-6_14(244-264)Online publication date: 18-Apr-2018
https://doi.org/10.1007/978-3-319-90050-6_14

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