research-article

Size Bounds for Factorised Representations of Query Results

Authors:

Jakub ZávodnýAuthors Info & Claims

ACM Transactions on Database Systems (TODS), Volume 40, Issue 1

Article No.: 2, Pages 1 - 44

https://doi.org/10.1145/2656335

Published: 25 March 2015 Publication History

Abstract

We study two succinct representation systems for relational data based on relational algebra expressions with unions, Cartesian products, and singleton relations: f-representations, which employ algebraic factorisation using distributivity of product over union, and d-representations, which are f-representations where further succinctness is brought by explicit sharing of repeated subexpressions.

In particular we study such representations for results of conjunctive queries. We derive tight asymptotic bounds for representation sizes and present algorithms to compute representations within these bounds. We compare the succinctness of f-representations and d-representations for results of equi-join queries, and relate them to fractional edge covers and fractional hypertree decompositions of the query hypergraph.

Recent work showed that f-representations can significantly boost the performance of query evaluation in centralised and distributed settings and of machine learning tasks.

Supplementary Material

a2-olteanu-apndx.pdf (olteanu.zip)

Supplemental movie, appendix, image and software files for, Size Bounds for Factorised Representations of Query Results

Download
70.06 KB

References

[1]

S. Abiteboul and N. Bidoit. 1986. Non first normal form relations: An algebra allowing data restructuring. J. Comput. Syst. Sci. 33, 3, 361--393.

Digital Library

[2]

S. Abiteboul, R. Hull, and V. Vianu. 1995. Foundations of Databases. Addison-Wesley.

Digital Library

[3]

S. Agrawal, V. Narasayya, and B. Yang. 2004. Integrating vertical and horizontal partitioning into automated physical database design. In Proceedings of the ACM SIGMOD International Conference on Management of Data (SIGMOD'04). 359--370.

Digital Library

[4]

A. Atserias, M. Grohe, and D. Marx. 2008. Size bounds and query plans for relational joins. In Proceedings of the 49^th Annual IEEE Symposium on Foundations of Computer Science (FOCS'08). 739--748.

Digital Library

[5]

G. Bagan, A. Durand, and E. Grandjean. 2007. On acyclic conjunctive queries and constant delay enumeration. In Proceedings of the 21^st International Workshop on Computer Science Logic (CSL'07). Lecture Notes in Computer Science, vol. 4646. Springer, 208--222.

Digital Library

[6]

N. Bakibayev, T. Kočiský, D. Olteanu, and J. Závodný. 2013. Aggregation and ordering in factorized databases. Proc. VLDB Endow. 6, 14, 1990--2001.

Digital Library

[7]

N. Bakibayev, D. Olteanu, and J. Závodný. 2012. FDB: A query engine for factorised relational databases. Proc. VLDB Endow. 5, 11, 1232--1243.

Digital Library

[8]

F. Bancilhon, P. Richard, and M. Scholl. 1982. On line processing of compacted relations. In Proceedings of the 8^th International Conference on Very Large Data Bases (VLDB'82). 263--269.

Digital Library

[9]

D. S. Batory. 1979. On searching transposed files. ACM Trans. Database Syst. 4, 4, 531--544.

Digital Library

[10]

P. A. Boncz, S. Manegold, and M. L. Kersten. 1999. Database architecture optimized for the new bottleneck: Memory access. In Proceedings of the 25^th International Conference on Very Large Data Bases (VLDB'99). 54--65.

Digital Library

[11]

R. K. Brayton. 1987. Factoring logic functions. IBM J. Res. Devel. 31, 2, 187--198.

Digital Library

[12]

D. Buchfuhrer and C. Umans. 2008. The complexity of Boolean formula minimization. In Proceedings of the 35^th International Colloquium on Automata, Languages and Programming (ICALP'08). 24--35.

Digital Library

[13]

K. Cattell, M. J. Dinneen, and M. R. Fellows. 1996. A simple linear-time algorithm for finding path-decompositions of small width. Inf. Process. Lett. 57, 4, 197--203.

Digital Library

[14]

L. Cerf, J. Besson, C. Robardet, and J.-F. Boulicaut. 2009. Closed patterns meet n-ary relations. ACM Trans. Knowl. Discov. Data 3, 1, 3.

Digital Library

[15]

H. Chen and M. Grohe. 2010. Constraint satisfaction with succinctly specified relations. J. Comput. Syst. Sci. 76, 8, 847--860.

Digital Library

[16]

P. Cudré-Mauroux, E. Wu, and S. Madden. 2009. The case for Rodentstore: An adaptive, declarative storage system. In Proceedings of the 4^th Biennial Conference on Innovative Data Systems Research (CIDR'09).

[17]

N. Dalvi and D. Suciu. 2007. Efficient query evaluation on probabilistic databases. VLDB J. 16, 4, 523--544.

Digital Library

[18]

C. Delobel. 1978. Normalization and hierarchical dependencies in the relational data model. ACM Trans. Database Syst. 3, 3, 201--222.

Digital Library

[19]

F. Geerts, B. Goethals, and T. Mielikäinen. 2004. Tiling databases. In Proceedings of the 7^th International Conference on Discovery Science (DS'04). Lecture Notes in Computer Science, vol. 3245, Springer, 278--289.

[20]

G. Gottlob. 2012. On minimal constraint networks. Artif. Intell. 191-192, 42--60.

Digital Library

[21]

G. Gottlob, N. Leone, and F. Scarcello. 2000. A comparison of structural CSP decomposition methods. Artif. Intell. 124, 2, 243--282.

Digital Library

[22]

T. J. Green, G. Karvounarakis, and V. Tannen. 2007. Provenance semirings. In Proceedings of the 26^th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS'07). 31--40.

Digital Library

[23]

M. Grohe and D. Marx. 2006. Constraint solving via fractional edge covers. In Proceedings of the 17^th Annual ACM-SIAM Symposium on Discrete Algorithm (SODA'06). 289--298.

Digital Library

[24]

M. Grund, J. Krüger, H. Plattner, A. Zeier, P. Cudre-Mauroux, and S. Madden. 2010. HYRISE—A main memory hybrid storage engine. Proc. VLDB Endow. 4, 2, 105--116.

Digital Library

[25]

F. Henglein and K. F. Larsen. 2010. Generic multiset programming with discrimination-based joins and symbolic Cartesian products. Higher-Order Symbol. Comput. 23, 3, 337--370.

Digital Library

[26]

T. Imielinski, S. Naqvi, and K. Vadaparty. 1991. Incomplete object-A data model for design and planning applications. In Proceedings of the ACM SIGMOD International Conference on Management of Data (SIGMOD'91). 288--297.

Digital Library

[27]

G. Jaeschke and H. J. Schek. 1982. Remarks on the algebra of non first normal form relations. In Proceedings of the 1^st ACM SIGACT-SIGMOD Symposium on Principles of Database Systems (PODS'82). 124--138.

Digital Library

[28]

W. Kent. 1983. A simple guide to five normal forms in relational database theory. Comm. ACM 26, 2, 120--125.

Digital Library

[29]

E. Korach and N. Solel. 1993. Tree-width, path-width, and cutwidth. Discr. Appl. Math. 43, 1, 97--101.

Digital Library

[30]

A. Makinouchi. 1977. A consideration on normal form of not-necessarily-normalized relation in the relational data model. In Proceedings of the 3^rd International Conference on Very Large Data Bases (VLDB'77). Vol. 3. 447--453.

Digital Library

[31]

D. Marx. 2010. Approximating fractional hypertree width. ACM Trans. Algor. 6, 2, 29:1--29:17.

Digital Library

[32]

H. Q. Ngo, D. T. Nguyen, C. Ré, and A. Rudra. 2013. Towards instance optimal join algorithms for data in indexes. http://arxiv.org/abs/1302.0914.

[33]

H. Q. Ngo, E. Porat, C. Ré, and A. Rudra. 2012. Worst-case optimal join algorithms (extended abstract). In Proceedings of the 31^st Symposium on Principles of Database Systems (PODS'12). 37--48.

Digital Library

[34]

D. Olteanu and J. Huang. 2008. Using OBDDs for efficient query evaluation on probabilistic databases. In Proceedings of the 2^nd International Conference on Scalable Uncertainty Management (SUM'08). 326--340.

Digital Library

[35]

D. Olteanu, C. Koch, and L. Antova. 2007. World-set decompositions: Expressiveness and efficient algorithms. In Proceedings of the 11^th International Conference on Database Theory (ICDT'07). 194--208.

Digital Library

[36]

D. Olteanu and J. Závodný. 2011. On factorisation of provenance polynomials. In Proceedings of the 3^rd USENIX Workshop on the Theory and Practice of Provenance.

[37]

D. Olteanu and J. Závodný. 2012. Factorised representations of query results: Size bounds and readability. In Proceedings of the 15^th International Conference on Database Theory (ICDT'12). 285--298.

Digital Library

[38]

Z. M. Ozsoyoglu and L.-Y. Yuan. 1987. A new normal form for nested relations. ACM Trans. Database Syst. 12, 1, 111--136.

Digital Library

[39]

J. Pearl. 1989. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Fransisco.

Digital Library

[40]

S. Rendle. 2013. Scaling factorization machines to relational data. Proc. VLDB Endow. 6, 5, 337--348.

Digital Library

[41]

P. Sen, A. Deshpande, and L. Getoor. 2010. Read-once functions and query evaluation in probabilistic databases. Proc. VLDB Endow. 3, 1, 1068--1079.

Digital Library

[42]

J. Shute, R. Vingralek, B. Samwel, B. Handy, C. Whipkey, E. Rollins, M. Oancea, K. Little-Field, D. Menestrina, S. Ellner, J. Cieslewicz, I. Rae, T. Stancescu, and H. Apte. 2013. F1: A distributed SQL database that scales. Proc. VLDB Endow. 6, 11, 1068--1079.

Digital Library

[43]

M. Stonebraker, D. J. Abadi, A. Batkin, X. Chen, M. Cherniack, M. Ferreira, E. Lau, A. Lin, S. Madden, E. O'Neil, P. O'Neil, A. Rasin, N. Tran, and S. Zdonik. 2005. C-store: A column-oriented DBMS. In Proceedings of the 31^st International Conference on Very Large Data Bases (VLDB'05). 553--564.

Digital Library

[44]

T. L. Veldhuizen. 2014. Triejoin: A simple, worst-case optimal join algorithm. In Proceedings of the 17^th International Conference on Database Theory (ICDT'14). 96--106.

Cited By

Birler AKemper ANeumann T(2024)Robust Join Processing with Diamond Hardened JoinsProceedings of the VLDB Endowment10.14778/3681954.368199517:11(3215-3228)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.14778/3681954.3681995
Makhija NGatterbauer W(2024)Minimally Factorizing the Provenance of Self-join Free Conjunctive QueriesProceedings of the ACM on Management of Data10.1145/36516052:2(1-24)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651605
Fan AKoutris PZhao H(2024)Tight Bounds of Circuits for Sum-Product QueriesProceedings of the ACM on Management of Data10.1145/36515882:2(1-20)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651588
Show More Cited By

Index Terms

Size Bounds for Factorised Representations of Query Results
1. Information systems
  1. Data management systems
2. Theory of computation
  1. Theory and algorithms for application domains
    1. Database theory
      1. Database query processing and optimization (theory)

Recommendations

Factorised representations of query results: size bounds and readability
ICDT '12: Proceedings of the 15th International Conference on Database Theory

We introduce a representation system for relational data based on algebraic factorisation using distributivity of product over union and commutativity of product and union.

We give two characterisations of conjunctive queries based on factorisations of ...
Size and treewidth bounds for conjunctive queries
PODS '09: Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems

This paper provides new worst-case bounds for the size and treewith of the result Q(D) of a conjunctive query Q to a database D. We derive bounds for the result size |Q(D)| in terms of structural properties of Q, both in the absence and in the presence ...
Size and Treewidth Bounds for Conjunctive Queries

This article provides new worst-case bounds for the size and treewith of the result Q(D) of a conjunctive query Q applied to a database D. We derive bounds for the result size |Q(D)| in terms of structural properties of Q, both in the absence and in the ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Database Systems

ACM Transactions on Database Systems Volume 40, Issue 1

March 2015

260 pages

ISSN:0362-5915

EISSN:1557-4644

DOI:10.1145/2751312

Editor:
Christian S. Jensen
Aalborg University, Denmark

Issue’s Table of Contents

Copyright © 2015 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 March 2015

Accepted: 01 July 2014

Revised: 01 May 2014

Received: 01 July 2013

Published in TODS Volume 40, Issue 1

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed

Funding Sources

EPSRC DTA

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

67
Total Citations
View Citations
625
Total Downloads

Downloads (Last 12 months)78
Downloads (Last 6 weeks)9

Reflects downloads up to 12 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

Birler AKemper ANeumann T(2024)Robust Join Processing with Diamond Hardened JoinsProceedings of the VLDB Endowment10.14778/3681954.368199517:11(3215-3228)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.14778/3681954.3681995
Makhija NGatterbauer W(2024)Minimally Factorizing the Provenance of Self-join Free Conjunctive QueriesProceedings of the ACM on Management of Data10.1145/36516052:2(1-24)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651605
Fan AKoutris PZhao H(2024)Tight Bounds of Circuits for Sum-Product QueriesProceedings of the ACM on Management of Data10.1145/36515882:2(1-20)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651588
Olteanu DGeerts FMartens W(2024)Recent Increments in Incremental View MaintenanceCompanion of the 43rd Symposium on Principles of Database Systems10.1145/3635138.3654763(8-17)Online publication date: 9-Jun-2024
https://dl.acm.org/doi/10.1145/3635138.3654763
Martens WNiewerth MPopp TRojas CVansummeren SVrgoč D(2024)Compact Path Representations for Graph Database Pattern Matching2024 IEEE 40th International Conference on Data Engineering Workshops (ICDEW)10.1109/ICDEW61823.2024.00059(379-380)Online publication date: 13-May-2024
https://doi.org/10.1109/ICDEW61823.2024.00059
Olteanu DVortmeier NŽivanović Ɖ(2024)Givens rotations for QR decomposition, SVD and PCA over database joinsThe VLDB Journal — The International Journal on Very Large Data Bases10.1007/s00778-023-00818-933:4(1013-1037)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/s00778-023-00818-9
Kara ANikolic MOlteanu DZhang H(2024)F-IVM: analytics over relational databases under updatesThe VLDB Journal — The International Journal on Very Large Data Bases10.1007/s00778-023-00817-w33:4(903-929)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/s00778-023-00817-w
Huang ZSen RLiu JWu E(2023)JoinBoost: Grow Trees over Normalized Data Using Only SQLProceedings of the VLDB Endowment10.14778/3611479.361150916:11(3071-3084)Online publication date: 24-Aug-2023
https://dl.acm.org/doi/10.14778/3611479.3611509
Huang ZLiu JAlabi DFernandez RWu E(2023)Saibot: A Differentially Private Data Search PlatformProceedings of the VLDB Endowment10.14778/3611479.361150816:11(3057-3070)Online publication date: 24-Aug-2023
https://dl.acm.org/doi/10.14778/3611479.3611508
Wang JTrummer IKara AOlteanu D(2023)ADOPT: Adaptively Optimizing Attribute Orders for Worst-Case Optimal Join Algorithms via Reinforcement LearningProceedings of the VLDB Endowment10.14778/3611479.361148916:11(2805-2817)Online publication date: 24-Aug-2023
https://dl.acm.org/doi/10.14778/3611479.3611489
Show More Cited By

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Issue’s Table of Contents