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Normalization of linear recursions based on graph transformations

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Information Systems and Data Management (CISMOD 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1006))

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Abstract

In this paper, we propose a new approach to generate normal form formulas for linear recursions based on graph transformations. We first extend the graph model proposed in [17] for representing linear recursive definitions completely, coupling with graph equivalence definitions. The new graph model is called IE-graph. Then three basic equivalence-preserving graph transformation techniques are newly defined on IE-graphs: (1) realigning; (2) reducing; (3) expanding. Based on these graph transformation techniques, we show that a general IE-graph can always be transformed equivalently into a set of disjoint unit cycles, called Normal IE-graph. The formula generated by our method is more efficient than that generated by Han and Zeng's method [7], because the formula generated by our method contains usually less variables in the recursive predicate.

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References

  1. F.Bancilhon and R.Ramekrishnan: An Amateur's Introduction to Recursive Query Processing Strategies” Proc. ACM SIGMOD, 1986

    Google Scholar 

  2. Bancilhon F., Maier D., Sagiv Y., Ullman J.D.: “Magic Set and Other Strange Ways to Implement Logic Programs”. Proceedings. ACM SIGACT-SIGMOD-SISART Symposium on Principles of Database Systems(PODS), (1986).

    Google Scholar 

  3. X.Du and N.Ishii: “Optimizing Linear Recursive Formulas by Detaching Isolated Variables”. IEICE TOIS Vol.E78-D No.5, May, 1995

    Google Scholar 

  4. X.Du and N.Ishii: “Reducing the Arity of Recursive Predicates by Realigning Some Predicates”, Proc. ICLP'95 Workshop on Deductive Database and Logic Programming. June 17, 1995

    Google Scholar 

  5. L.Henschen and S.Naqvi: On Compiling Queries in Recursive First-Order Data base, JACM vol.51 (1984)

    Google Scholar 

  6. Jiawei Han: Compiling General Linear Recursions by Variable Connection Graph Analysis, Comput. Intell. 5, 12–31, (1989)

    Google Scholar 

  7. Jiawei Han, Kangsheng Zeng: Automatic Generation of Compiled Forms for Linear Recursions, Information Systems, Vol.17, No.4, pp.299–322, (1992)

    Article  Google Scholar 

  8. Y.Ioannidis: A Time Bound on the Materialization of some Recursively Defined Views, Proceedings of Very Large Data Bases(VLDB), (1985)

    Google Scholar 

  9. Lakshmanan, L.V.S., Hernandez,H.J.: “Structural Query Optimization — A Uniform Framework for Semantic Query Optimization in Deductive Databases”, Proc. ACM Symposium on Principles of Database Systems(PODS), (1991), pp.102–114.

    Google Scholar 

  10. W.Lu, D.L.Lee, J.Han: A Study on the Structure of Linear Recursion, IEEE Trans. Knowledge and Data engineering, Vol.6, No.5, pp.723–737 (1994)

    Article  Google Scholar 

  11. J.Naughton: Data Independent Recursion in Deductive Database, Proceedings ACM SIGACT-SIGMOD-SIGART Symp. Principles of Database Systems(PODS), (1986).

    Google Scholar 

  12. J.Naughton: One-Side Recursions, Proc. 6th ACM SIGACT-SIGMOD-SIGART Symp. Principles of Database Systems(PODS), pp.340–348 (1987)

    Google Scholar 

  13. J.Naughton: Minimizing Function-Free Recursive Inference Rules. J. ACM Vol.36, No.1, pp.69–91 (1989)

    Article  Google Scholar 

  14. J.Naughton, R.Ramakrishnan, Y.Sagiv, J.D.Ullman: Argument Reduction by Factoring, Proc. the 15th Int. Conf. on Very Large Data Bases(VLDB), pp.173–182 (1989)

    Google Scholar 

  15. S. Seshadri, J.F.Naughton: “On the Expected Size of Recursive Datalog Queries”, Proc. ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS), pp.268–279 (1991).

    Google Scholar 

  16. J.D.Ullman: Principles of Database and Knowledge-Base Systems, Vol.II, Computer Science Press, (1989)

    Google Scholar 

  17. C.Yong, H.J. Kim, L.J.Henschen, and J. Han: Classification and Compilation of Linear Recursive Queries in Deductive Databases. IEEE Transactions on Knowledge and Data Engineering, Vol.4, No.1, pp.52–67 (1992)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Intelligence and Computer Science, Nagoya Institute of Technology, 466, Nagoya, Japan

    Xiaoyong Du & Naohiro Ishii

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  1. Xiaoyong Du
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  2. Naohiro Ishii
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Subhash Bhalla

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© 1995 Springer-Verlag Berlin Heidelberg

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Du, X., Ishii, N. (1995). Normalization of linear recursions based on graph transformations. In: Bhalla, S. (eds) Information Systems and Data Management. CISMOD 1995. Lecture Notes in Computer Science, vol 1006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60584-3_38

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  • DOI: https://doi.org/10.1007/3-540-60584-3_38

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60584-3

  • Online ISBN: 978-3-540-47799-0

  • eBook Packages: Springer Book Archive

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