This Article 
 Bibliographic References 
 Add to: 
The Strong Partial Transitive-Closure Problem: Algorithms and Performance Evaluation
August 1996 (vol. 8 no. 4)
pp. 617-629

Abstract—The development of efficient algorithms to process the different forms of transitive-closure (TC) queries within the context of large database systems has recently attracted a large volume of research efforts. In this paper, we present two new algorithms suitable for processing one of these forms, the so called strong partially instantiated transitive closure, in which one of the query's arguments is instantiated to a set of constants and the processing of which yields a set of tuples that draw their values from both of the query's instantiated and uninstantiated arguments. These algorithms avoids the redundant computations and high storage cost found in a number of similar algorithms. Using simulation, this paper compares the performance of the new algorithms with those found in literature and shows clearly the superiority of the new algorithms.

[1] R. Agrawal, S. Dar, and H. Jagadish, “Direct Transitive Closure Algorithms: Design and Performance Evaluation,” ACM Trans. Database Systems, vol. 15, no. 3, pp. 427-458, Sept. 1990.
[2] R. Agrawal and H.V. Jagadish, "Hybrid Transitive Closure Algorithms," Proc. 16th VLDB Conf.,Brisbane, Australia, pp. 326-334, 1990.
[3] F. Bancilhon, D. Maier, Y. Sagiv, and J.D. Ullman, "Magic Sets and Other Strange Ways to Implement Logic Programs," Proc. Fifth ACM PODS Symp. Principles of Database Systems, pp. 1-15, 1986.
[4] F. Bancilhon and R. Ramakrishnan,“An amateur’s introduction to recursive query processing strategies,” Proc. 1986 ACM-SIGMOD Int’l Conf. Management Data, pp. 16-52,Washington, DC, May 1986.
[5] S. Dar and H.V. Jagadish, "A Spanning Tree Transitive Closure Algorithm," Proc. Int'l Conf. Data Eng., IEEE, 1992.
[6] S. Dar and R. Ramakirishnan, “A Performance Study of Transitive Closure Algorithms,” Proc. ACM-SIGMOD 1994 Int'l Conf. Management of Data, pp. 454-465, 1994.
[7] D.J. DeWitt, R.H. Katz, F. Olken, L.D. Shapiro, and M.R. Stonebraker, “Implementation Techniques for Main Memory Database Systems,” Proc. ACM SIGMOD, 1984.
[8] J. Han, G. Qadah, and C. Chaou, "The Processing of the Transitive Closure Queries," Proc. 1988 Int'l Conf. Extending Database Technology, pp. 48-75,Venice, Italy, Mar. 1988.
[9] Y. Ioannidis and R. Ramakirishnan, “Efficient Transitive Closure Algorithms,” Proc. 14th VLDB Conf., pp. 382-394, 1988.
[10] Y. Ioannidis, R. Ramakrishnan, and L. Winger, "Transitive Closure Algorithms Based on Graph Traversal," ACM Trans. Database Systems, vol. 18, no. 3, Sept. 1993.
[11] Y.E. Ioannidis, "On the Computation of the Transitive Closure of Relational Operators," Proc. 12th Int'l Conf. VLDB, pp. 403-411,Kyoto, Japan, 1986.
[12] H. Jagadish, “A Compression Technique to Materialize Transitive Closure,” ACM Trans. Database Systems, vol. 15, no. 4, pp. 558-598, Dec. 1990.
[13] H. Jakobsson, "Mixed Approach Algorithms for Transitive Closure," Proc. 10th ACM Symp. Principles of Database Syst., pp. 199-205,Denver, Colo., 1991.
[14] H. Jakobsson, "On Tree-Based Techniques for Query Evaluation," Proc. 11th ACM Symp. Principles of Database Syst., pp. 380-392, 1992.
[15] B. Jiang, “A Suitable Algorithm for Computing Partial Transitive Closures in Databases” Proc. IEEE Sixth Int'l Conf. Data Eng., pp. 264-271, 1990.
[16] G. Qadah, L. Henschen, and J. Kim, “Efficient Algorithms for the Instantiated Transitive Closure Queries,” IEEE Trans. Software Eng., vol. 17, no. 3, pp. 296-309, Mar. 1991.
[17] G. Qadah and J. Kim, "The Processing of Instantiated Transitive-Closure Queries on Uniprocessor and Shared-Nothing Multiprocessor Systems," J. Data and Knowledge Eng., no. 8, pp. 57-89, 1992.
[18] G.Z. Qadah and K.B. Irani,“The join algorithms on a shared-memory multiprocessor database machine,” IEEE Trans. Software Engineering, vol. 14, no. 11, pp. 1,668-1,683, Nov. 1988.
[19] L. Shapiro, "Join Processing in Database Systems with Large Main Memories," ACM Trans. Database Systems, vol. 11, no. 3, Sept. 1986.
[20] R. Tarjan, "Depth-First Search and Linear Graph Algorithms," SIAM J. Comput., no. 1, pp. 146-160, 1972.
[21] I.H. Toroslu and G.Z. Qadah, "New Transitive Closure Algorithm for Recursive Query Processing in Deductive Databases," Proc. Fourth IEEE Int'l Conf. Tools With AI, pp. 268-275,Arlington, Va., 1992.
[22] I. Toroslu and G. Qadah, “The Efficient Computation of Strong Partial Transitive-Closures,” Proc. IEEE Ninth Int'l Conf. Data Eng., pp. 530-537, 1993.
[23] I.H. Toroslu, G.Z. Qadah, and L. Henschen, "An Efficient Database Transitive Closure Algorithm," J. Applied Intelligence, vol. 4, pp. 205-218, 1994.
[24] J.D. Ullman and M. Yannakakis, "The Input/Output Complexity of Transitive Closure," Proc. Ninth ACM-SIGMOD Int'l Conf. Management Data, pp. 44-53,Atlantic City, N.J., 1990.
[25] J.D. Ullman and M. Yannakakis, "High Probability Parallel Transitive Closure Algorithms," SIAM J. Computing, vol 20, no. 1, pp. 100-125, Feb. 1991.
[26] P. Valduriez and H. Boral, "Evaluation of Recursive Queries Using Join Indices," Proc. First Int'l Expert Database Syst. Conf., pp. 197-208,Charleston, S.C., 1986.

Index Terms:
Database algorithms, deductive databases, performance evaluation, recursive rules, and transitive closure queries.
Ismail H. Toroslu, Ghassan Z. Qadah, "The Strong Partial Transitive-Closure Problem: Algorithms and Performance Evaluation," IEEE Transactions on Knowledge and Data Engineering, vol. 8, no. 4, pp. 617-629, Aug. 1996, doi:10.1109/69.536254
Usage of this product signifies your acceptance of the Terms of Use.