Transitive closure and the LOGA+-strategy for its efficient evaluation

  • W. Yan
  • N. Mattos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 364)


One of the key problems when extending relational database query languages to include deductive capabilities, is to provide them with efficient methods for answering recursive queries. During the last few years many algorithms have been proposed to deal with transitive closure computation of a relation. In this paper, we discuss some important criteria for developing transitive closure algorithms. After presenting these issues, we describe an algorithm for transitive closure computation and show some results of performance measurements comparing several algorithms.


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  1. [AJ87]
    Agrawal, R., Jagadisch, H.: Direct Algorithms for Computing the Transitive Closure of Database Relations, in: Proc. of the 13th VLDB Conference, Brighton 1987, pp. 255–266.Google Scholar
  2. [Ba85]
    Bayer, R.: Database Technology for Expert Systems, in: Proc. Gl-Conference on Knowledge-Based Systems, Informatik-Fachbereichte 112, Springer-Verlag, Munich, Oct. 1985, pp. 1–16.Google Scholar
  3. [Ba86]
    Bancilhon, F.: Naive Evaluation of Recursively Defined Relations, in: On Knowledge Base Management Systems — Integrating Database and Al Systems, (Ed: Brodie and Mylopoulos), Springer-Verlag, 1986, pp. 165–178.Google Scholar
  4. [BMSU86]
    Bancilhon, F., Maier, D., Sagiv, Y., Ullman, J.: Magic Sets and Other Strange Ways to Implement Logic Programs, in: Proc. of the Fifth ACM SIGACT-SIGMOD Symposium on Prinziples of Database Systems, Cambridge, Massachusetts, March, 1986.Google Scholar
  5. [BR86]
    Bancilhon, F., Ramakrishnan, R.: An Amateur's Introduction to Recursive Query Processing Strategies, in: Proc. of SIGMOD '86, Inter. Conf. on Management of Data, SIGMOD Record, Vol. 15, No. 2, June 1986, pp. 16–52.Google Scholar
  6. [BR88a]
    Bancilhon, F., Ramakrishnan, R.: Perfoemance Evaluation of Data Intensive Logic Programs, in: "Foundations of Deductive Databases and Logic Programming" (Ed: Minker, J.), Morgan Kaufmann Publishers, 1988, pp. 439–511.Google Scholar
  7. [BR88b]
    Beeri, C., Ramakrishnan, R.: On the Power of Magic, Computer Sciences Technical Report #770, University of Wisconsin-Madison, to appear in the Journal of Logic Programming.Google Scholar
  8. [Da87]
    Data, C.J.: A Guide to INGRES, Addison-Wesley Publishing Company, 1987.Google Scholar
  9. [DS86]
    Dayal, U., Smith, J.: PROBE: A Knowledge-Oriented Database, in: On Knowledge Base Management Systems (Ed: Brodie and Mylopoulos), Springer-Verlag, 1986, pp. 227–257.Google Scholar
  10. [GMN84]
    Gallaire, H., Minker, J., Nicolas, J.M.: Logic and Databases: A Deductive Approach, in: ACM Computing Surveys, Vol. 16, No. 2, June 1984, pp. 153–186.Google Scholar
  11. [He86]
    Heigert, J.: Efficient Algorithms for Relational Database Systems Supporting Recursion (in German), TUM-18613, TU Munich, July 1986.Google Scholar
  12. [HL86]
    Han, J., Lu, H.: Some Performance Results on Recursive Query Processing in Relational Database Systems, in: IEEE Proc. of Inter. Conf. on Data Engineering, Los Angeles, Feb. 1986.Google Scholar
  13. [HQC88]
    Han, J., Qadah, G., Chaou, C.: The Processing and Evaluation of Transitive Closure Queries, iin: Advances in Database Technology — EDBT '88, Inter. Conf. on Extending Database Technology, Venice, Italy, March 1988, Sringer-Verlag, pp. 49–75.Google Scholar
  14. [Io86]
    Ioannidis, Y.: On the Computation of the Transitive Closure of Relational Operators, in: Proc. of the 12th VLDB Conference, Kyoto, 1986, pp. 403–411.Google Scholar
  15. [IW88]
    Ioannidis, Y., Wong, E.: Transforming Nonlinear Recursion to Linear Recursion, in: Proc. of the Second Inter. Conf. on Expert Database Systems, EDBS '88, Tysons Corner, Virginia, Apr. 1988.Google Scholar
  16. [JAN87]
    Jagadish, H., Agvawal, R., Ness, L.: A Study of Transitive Closure as a Recursion Mechanism, in: Proc. of ACM SIGMOD 1987 Annual Conference, San Francisco, May 1987, pp. 331–344.Google Scholar
  17. [KL86]
    Kifer, M., Lozinskii, E.: A Framework for an Efficient Implementation of Deductive Databases, in: Proc. of Advanced Database Symposium, Tokyo, 1986.Google Scholar
  18. [LMR87]
    Lu, H., Mikkilineni, K., Richadson, J.: Design and Evaluation of Algorithms to Compute the Transitive Closure of a Database Relation, in: Proc. of the Third Inter. Conf. on Data Engineering, Los Angeles, Feb. 1987, pp. 112–119.Google Scholar
  19. [SZ87]
    Sacca, D., Zaniolo, C.: Magic Counting Methods, in: Proc. of ACM SIGMOD 1987 Annual Conference, San Francisco, May 1987, pp. 49–59.Google Scholar
  20. [Vi86]
    Vieille, L.: Recursive Axioms in Deductive Databases: the Query/Subquery Approach, in: Proc. of First Inter. Conf. on Expert Database Systems, Charleston, 1986, pp. 179–193.Google Scholar
  21. [Ya87]
    Yan, W.: Analysis of Different Strategies for the Processing Recursive Queries in Deductive Database Systems (in German), Technical report, University of Kaiserslautern, Nov. 1987.Google Scholar
  22. [Ya89]
    Yan, W.: An Overview of Existing Strategies for the Evaluation of Recursive Queries (in German), Internal Report, University of Kaiserslautern, in preparation.Google Scholar
  23. [ZY87]
    Zhang, W., Yu, C.: A Necessary Condition for a Doubly Recursive Rule to be Equivalent to a Linear Recursive Rule, in: Proc. of ACM SIGMOD 1987 Annual Conference, San Francisco, May 1987, pp. 345–356.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • W. Yan
    • 1
  • N. Mattos
    • 2
  1. 1.Central South University of TechnologyChangshaChina
  2. 2.Department of Computer ScienceUniversity of KaiserslauternKaiserslauternWest Germany

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