Skip to main content
SpringerLink
Log in

Magic sets revisited

  • Published:
Journal of Computer Science and Technology Aims and scope Submit manuscript

Abstract

This paper distinguishes among three kinds of linear recursions: canonical strongly linear recursion (CSLR), non-interdependent linear recursion (NILR) and interdependent linear recurstion (ILR) and presents an optimal algorithm for each. First, for the CSLRs, the magic-set method is refined in such a way that queries can be evaluated efficiently. Then, for the NILRs and ILRs, the concept of query dependency graphs is introduced to partition the rules of a program into a set of CSLRs and the computation is elaborated so that the oplimization for CSLRs can also be applied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bancilhon F, Ramakrishnan R. An Amateur’s introduction to recursive query processing strategies. InProc. 1986 ACM-SIGMOD Conf. on Management of Data, Washington, D.C., May 1986, pp.16–52.

  2. Han J, Zeng K, Lu T. Normalization of linear recursion in deductive databases. InProc. of the 9th Int’l Conf. on Data Engineering, Vienna, Austria, April 1993, pp.559–567.

  3. Han J, Chen S. Graphic representation of linear recursive rules.International Journal of Intelligence System, 1992, 7: 317–337.

    Article  MATH  Google Scholar 

  4. Henschen L J, Naqvi S. On compiling queries in recursive first-order database.J. ACM, 1984, 31(1): 47–85.

    Article  MATH  MathSciNet  Google Scholar 

  5. Ioannidis Y, Wong E. Towards an algebraic theory of recursion.Journal of the Association for Coinpuling Machinery, 1991, 38(2): 329–381.

    MATH  MathSciNet  Google Scholar 

  6. Knuth D E. The Art of Computer Programming. Addison-Wesley Series in Computer Science and Information Processing, 1968, pp.257–265.

  7. Nejdl W. Recursive strategies for answering recursive queries—The RQA/FQI strategy. InProc. 13th VLDB Conf., Brighton, 1987, pp.43–50.

  8. Marchetti-Spaccamela A, Pelaggi A, Sacca D. Worst case complexity analysis of methods for logic query implementation. InProc. ACM-PODS 87,

  9. Chang C. On the Evaluation of Queries Containing Derived Relations in Relational Database. Advances in Data Base Theory, Vol.1, Plenum, 1981.

  10. Chen Y, Härder T. Improving RQA/FQI recursive query algorithm. InProc. ISMM-First Int’l Conf. on Information and Knowledge Management, Baltimore, Maryland, Nov. 1992.

  11. Chen Y. A bottom-up query evaluation method for stratified databases. In Proc. 9th Int’l Conf. on Data Engineering, Vienna, Austria, April 1993, pp.568–575.

  12. Chen Y, Härder T. On the optimal top-down evaluation of recursive queries. InProc. of 5th Int’l Conf. on Database and Expert Systems Applications, Athens, Greece, Sept. 1994, pp.47–56.

  13. Chen Y, Härder T. An optimal graph traversal algorithm for evaluating linear binary-chain programs. InProc. CIKM’94—The 3th Int’l Conf. on Information and Knowledge Management, Gaithersburg, Maryland, Nov. 1994, pp.34–41.

  14. Chen Y, Härder T. Graph traversal and linear binary-chain programs. ZRI-Report 4/94, University of Kaiserslautem, 1994.

  15. Chen Y. Processing of recursive rules in knowledge-based systems—Algorithms for handling recursive rules and negative information and performance measurements. Ph.D. Thesis, Computer Science Department, University of Kaiserslautem, Germany, Feb. 1995.

    Google Scholar 

  16. Sacca D, Zaniolo C. Implementation of recursire queries for a data language based on pure Horn logic. InProc. the 4th Int’l Conf. on Logic Programming, Univ. of Melbourne, 1987, pp.104–135.

  17. Bancilhon F. Naive Evaluation of Recursively Defined Relations. On Knowledge Base Management Systems-Integrating Database and AI Systems. Springer-Verlag, 1985.

  18. BancilhonF, Maier D, Sagiv Y, Ullman J D. Magic sets and other strange ways to implement logic programs. InProc. 5th ACM Symp. Principles of Database Systems, Cambridge, MA, March 1986, pp.1–15.

  19. Beeri C, Ramakrishnan R. On the power of magic.J. Logic Programming, 1991, 10: 255–299.

    Article  MATH  MathSciNet  Google Scholar 

  20. Ullman J D. Implementation of logical query languages for databases.ACM Trans. Database Systems, 1985, 10(3).

  21. Aly H, Ozsoyoglu Z M. Synchronized Counting Method. InProc. the 5th Int’l Conf. on Data Engineering, Los Angeles, 1989.

  22. Sacca D, Zaniolo C. On the implementation of a simple class of logic queries for databases. InProc. the 5th ACM SIGMOD-SIGACT Symp. on Principles of Database Systems, 1986, pp.16–23.

  23. Shapiro S, McKay. Inference with recursive rules. InProc. of the 1st Annual National Conference on Artificial Intelligence, 1980.

  24. Marchetti-Spaccamela A, Pelaggi A, Sacca D. Comparison of methods for logic-query implementation.J. Logic Programming, 1991, 10: 333–360.

    Article  MATH  MathSciNet  Google Scholar 

  25. Haddad R W, naughton J F. Counting method for cyclic relations. InProc. the 7th ACM SIGMOD-SIGACT Symp. on Principles of Database Systems, 1986, pp.16–23.

  26. Han J, Henschen L J. The level-cycle merging method. InProc. of the 1st Int’l Conf. on Deductive and Object-Oriented Databases, Kyoto, 1989.

  27. Vieille L. From QSQ to QoSaQ: Global optimization of recursive queries. InProc. 2nd Int’l Conf. on Expert Database System, Kerschberg L (ed.), Charleston, 1988.

  28. Ceri S, Gottlob G, Tanca L. Logic Programming and Databases. Springer-Verlag, Berlin, 1990.

    Google Scholar 

  29. Balbin G S, Port K R, Meenakshi. Efficient bottom-up computation of queries on stratified databases.J. Logic Programming, 1991, 10: 295–344.

    Article  MathSciNet  Google Scholar 

  30. Bancilhon F, Ramakrishnan R. Performance evaluation of data intensive logic programs. InPreprints of Workhop on Foundations of Deductive Databases and Logic Programming, August 1986.

  31. Tarjan R. Depth-first search and linear graph algorithms.SIAM J. Compt., 1972, 1(2).

  32. Wu C, Henschen L J. Answering linear recursive queries in cyclic databases. InProc. the 1988 Int’l Conf. on Fifth Gen. Computer Systems, Tokyo, 1988.

Download references

Author information

Author notes

  1. Chen Yangjun

    Present address: Dept. of Computer Science, Technical University Chemnitz-Zwickau, 09107, Chemnitz, Germany

Authors and Affiliations

  1. Technical Institute of Changsha, 410073, Changsha

    Chen Yangjun

Authors
  1. Chen Yangjun
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Chen Yangjun received his B.S. degree in information system engineering from the Technical Institute of Changsha, China, in 1982, and his Diploma and Ph.D. degrees in computer science from the University of Kaiserslautern, Germany, in 1990 and 1995, respectively. Dr. Chen is currently an Assistant Professor of the Technical University of Chemnitz-Zwickau, Germany. His research interests include deductive databases, federative databases, constraint satisfaction problem, graph theory and combinatorics. He has about 30 publications in these areas.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, Y. Magic sets revisited. J. of Comput. Sci. & Technol. 12, 346–365 (1997). https://doi.org/10.1007/BF02943154

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02943154

Keywords

Search

Navigation