Efficient Management of K-Level Transitive Closure

  • Keh-Chang Guh
  • Pintsang Chang
Conference paper

Abstract

A k-level transitive closure of a directed graph is all pairs of vertices (x, y) such that there exists at least a path from x to y of length d, d≤k. Multiple edges between a pair of vertices are allowed in a graph. This paper presents a data structure to store materialized k-level transitive closure such that retrievals and updates of a k-level transitive closure with path information being kept may be performed efficiently.

Keywords

Directed Path Query Processing Transitive Closure Multiple Edge Data Engineer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    Agrawal, R., Borgida A., and Jagadish, H., “Efficient management of transitive relationships in large data and knowledge bases,” ACM SIGMOD 1989, pp. 253-262.Google Scholar
  2. 2.
    Agrawal, R. “Alpha: An extension of relational algebra to express a class of recursive queries,” in Proceedings of Third International Conference on Data Engineering, Feb. 3–5, 1987, Los Angeles, pp. 580-590.Google Scholar
  3. 3.
    Blakeley, J. A., Coburn, N., and Larson, P., “Updated derived relations: Detecting irrelevant and autonomously computable updates,” ACM Transactions on Database Systems, Vol. 14, No. 3, September 1989, pp. 369–400.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bancilhon, F. and Ramakrishnan, R., “An amateur’s introduction to recursive query processing strategies,” ACM SIGMOD, 1986, pp. 16-52.Google Scholar
  5. 5.
    Chang, P. and Henschen, L. J., “Parallel transitive closure and transitive reduction algorithms,” PARBASE-90, International Conference on Databases, Parallel Architectures, and Their Applications, March 1990, pp. 152-154.Google Scholar
  6. 6.
    Deo, N., Graph Theory with Application to Engineering and Computer Science, Prentice-Hall, Inc., Englewood Cliffs, N. J.Google Scholar
  7. 7.
    Enbody, R. J. and Du, H. C., “Dynamic hashing schemes,” ACM Computing Surveys, Vol. 20, No. 2, June 1988, pp. 85–113.CrossRefGoogle Scholar
  8. 8.
    Guh, K. C. and Chavarria, J., “A parallel processing strategy for computing transitive closure of a database relation,” PARBASE-90, International Conference on Databases, Parallel Architectures and Their Applications, March 1990, pp. 37-43.Google Scholar
  9. 9.
    Guh, K. C., Sun, C., and Yu, C. T., “Real time retrieval and update of materialized transitive closure,” IEEE Seventh International Conference on Data Engineering, 1991,pp. 690-697.Google Scholar
  10. 10.
    Guh, K. C. and Yu, C. T., “Evaluation of transitive closure in distributed database systems,” IEEE Journal on Selected Areas in Communications, Vol. 7, No. 3, April 1989, pp. 399–407.CrossRefGoogle Scholar
  11. 11.
    Guh, K. C. and Yu, C. T., “Efficient management of materialized generalized transitive closure in centralized and parallel environments,” IEEE Transactions on Knowledge and Data Engineering (to appear).Google Scholar
  12. 12.
    Han, J. and Lu, W., “Asynchronous chain recursions,” IEEE Transactions on Knowledge and Data Engineering, Vol. 1, No. 2, June 1989, pp. 185–195.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Henschen, L. J. and Naqvi, S. A., “On compiling queries in recursive first-order databases,” J. ACM, Vol. 31, No. 1, Jan. 1984, pp. 47–85.MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Ioannidis, Y. E. and Ramakrishnan, R., “Efficient transitive closure algorithms,” The 14th International Conference on Very Large Data Bases, Los Angeles, August, 1988,pp. 382-394.Google Scholar
  15. 15.
    Ioannidis, Y. E. and Wong, E., “Transforming nonlinear recursion to linear recursion,” Second International Conference on Expert Database Systems, April, 1988, pp. 187-207.Google Scholar
  16. 16.
    Jagadish, H. V., Agrawal, R., and Ness, L., “A study of transitive closure as a recursion mechanism,” ACM SIGMOD, San Francisco, May 1987, pp. 331-344.Google Scholar
  17. 17.
    Jagadish, H. V., “A compressed transitive closure technique for efficient fixed-point query processing,” Proceedings of the Second International Conference on Expert Database Systems, April 1988, pp. 209-223.Google Scholar
  18. 18.
    Kifer, M. and Lozinskii, EX., “A frame work for an efficient implementation of deductive database,” In Proceedings of the Advanced Database Symposium, Tokyo, Japan, 1986.Google Scholar
  19. 19.
    Lu, H., Mikkilineni, K., and Richardson, J. P., “Design and evaluation of algorithms to compute the transitive closure of a database relation,” Third International Conference on Data Engineering, Los Angeles, Feb. 3–5, 1987, pp. 112-119.Google Scholar
  20. 20.
    Troy, D., Yu, C., and Zhang, W. “Linearization of nonlinear recursive rules,” IEEE Transactions on Software Engineering, Vol. 15, No. 9, September 1989, pp. 1109–1119.MathSciNetCrossRefGoogle Scholar
  21. 21.
    Valduriez, P. and Khoshafian, S., “Transitive closure of transitively closed closed relations,” Second International Conference on Expert Database Systems, April 1988, pp. 177-185.Google Scholar
  22. 22.
    Zhang, W., Yu, C. T., and Troy, D., “A necessary and sufficient condition for a doubly recursive rule to be equivalent to a linear recursive rule,” ACM Transactions on Database Systems, Vol. 15, No. 3, September 1990, pp. 459–482.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1992

Authors and Affiliations

  • Keh-Chang Guh
    • 1
  • Pintsang Chang
    • 2
  1. 1.Department of Electrical Engineering and Computer ScienceUniversity of Wisconsin — MilwaukeeMilwaukeeUSA
  2. 2.COVIA PartnershipRosemontUSA

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