This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Study on the Structure of Linear Recursion
October 1994 (vol. 6 no. 5)
pp. 723-737

We study a general class of single linear recursions and the properties of their expansions by analyzing the structures of the recursions. We show that the expansions of a linear recursion of this class are very regular in that the variable connections are heavily shared and change periodically with respect to the expansions. The variable connections can be precisely characterized as static bindings and chain connections. We conclude that a single linear recursion under our assumptions either is bounded or can be expressed as chain recursions. This study contributes to query processing, because it provides the basis for rule compilation as a general and powerful technique for query processing. Combined with query information, the expansion properties of the recursion provide optimized query-processing plans.

[1] H. Aly and Z. M. Ozsoyoglu, "Synchronized counting method,"Proc. 5th Int. Conf. Data Eng., 1989, pp. 366-373.
[2] F. Bancilhon and R. Ramakrishnan, "An amateur's introduction to recursive query processing strategies," inProc. 1986 ACM-SIGMOD Conf. Management of Data(Washington, DC), May 1986, pp. 16-52.
[3] C. Beeri and R. Ramakrishnan, "On the power of magic," inProc. 6th ACM Symp. Principles of Database Syst.(San Diego, CA), Mar. 1987, pp. 269-283.
[4] J. Han, "Compiling general linear recursions by variable connection graph analysis,"Comput. Intell., vol. 5, no. 1, pp. 12-31, 1989.
[5] J. Han and L. J. Henschen, "The level-cycle merging method,"Proc. 1st Int. Conf. Deductive and Object-Oriented Databases (DOOD'89), 1989, pp. 113-129.
[6] J. Han and L. Liu, "Processing multiple linear recursions,"IEEE Trans. Software Eng., vol. 17, pp. 1241-1252, 1991.
[7] J. Han and L. Liu, "Asynchronous chain recursions,"IEEE Trans. Knowl. Data Eng., vol. 1, pp. 185-195, June 1989.
[8] L. J. Henschen and S. Naqvi, "On compiling queries in recursive first-order databases,"J. ACM, vol. 1, no. 1, pp. 47-85, 1984.
[9] Y. E. Ioannidis, "A time bound on the materialization of some recursively defined views,"Proc. 11th Int. Conf. Very Large Data Bases, 1985, pp. 219-225.
[10] H. V. Jagadish and R. Agrawal, "A study of transitive closure as a recursion mechanism," inProc. 1987 ACM SIGMOD Conf. (San Francisco, CA), 1987, pp. 331-334.
[11] D. L. Lee and W. Lu, "Graph modeling and analysis of linear recursive queries,"Proc. Int. Conf. Database, Parallel Architectures, and Their Applic. (PARBASE-90), 1990, pp. 44-53.
[12] D. L. Lee and W. Lu, "Graph modeling and analysis of linear recursive queries,"Database: Theory, Design and Aplications, 1991, pp. 151-167.
[13] Y. Y. Leung and D. L. Lee, "Logic approaches for deductive databases,"IEEE Expert, vol. 3, pp. 64-75, Winter 1988.
[14] W. Lu and D. L. Lee, "Recursive query processing based on program structure,"Methodogies for Intell. Syst., vol. 5, pp. 174-181, 1990.
[15] W. Lu and D. L. Lee, "The design of a recursive query processor,"Proc. Int. Conf. Data Base and Expert Syst. Applic. (DEXA '90), 1990, pp. 448-455.
[16] W. Lu and D. L. Lee, "Structural study and query processing of commutative multiple linear recursions,"Proc. Int. Symp. Computational Intell. (CI'90), Milan, Italy, Sept. 1990.
[17] W. Lu and D. Lee, "Characterization and Processing of Simple Prefixed-Chain Recursion,"Information Sciences, Feb. 1993, pp. 247-281.
[18] W. Lu, D. L. Lee, I.-M. Hsu, and S.-S. Wei, "Minimizing search redundancy in processing bounded recursions,"Proc. CIPS Edmonton '90 Inform. Technol. Conf., Edmonton, AB, Canada, Oct. 1990.
[19] J. F. Naughton, "Minimizing function-free recursive inference rules,"J. ACM, vol. 36, no. 1, pp. 69-91, 1989.
[20] J. F. Naughton, "Compiling separable recursions," inProc. 1988 ACM-SIGMOD Conf. Management of Data(Chicago, IL), June 1988, pp. 312-319.
[21] J. F. Naughton, "One-sided recursions," inProc. 6th ACM Symp. Principles of Database Syst., San Diego, CA, Mar. 1987, pp. 340- 348.
[22] J. F. Naughton, R. Ramakrishnan, Y. Sagiv, and J. D. Ullman, "Efficient evaluation of right-, left-, and multi-linear rules," inProc. 1989 ACM-SIGMOD Conf. Management of Data(Portland, OR), June 1989, pp. 235-242.
[23] J. F. Naughton and Y. Sagiv, "A decidable class of bounded recursions," inProc. 6th ACM Symp. Principles of Database Syst.(San Diego, CA), Mar. 1987, pp. 214-226.
[24] J. D. Ullman, "Implementation of logical query languages for databases,"ACM TODS, vol. 10, no. 3, pp. 289-321, 1985.
[25] M. Y. Vardi, "Decidability and undecidability results for boundedness of linear recursive queries," inProc. ACM Symp. Principles of Database Syst., 1988, pp. 341-350.
[26] C. Youn, L. J. Henschen, and J. Han, "One-directional recursive formulas,"Proc. 3rd Int. Conf. Data Knowl. Bases, 1988, pp. 69-78.
[27] C. Youn, L. Henschen, and J. Han "A classification of recursive formulas in deductive databases," inProc. ACM-SIGMOD Conf. Management of Data, Chicago, IL, June 1988.

Index Terms:
query processing; database theory; optimisation; deductive databases; linear recursion; expansions; variable connections; static bindings; chain connections; chain recursions; query processing; rule compilation; query information; optimized query-processing plans; deductive database; logic database; rule classification
Citation:
W. Lu, D.L. Lee, J. Han, "A Study on the Structure of Linear Recursion," IEEE Transactions on Knowledge and Data Engineering, vol. 6, no. 5, pp. 723-737, Oct. 1994, doi:10.1109/69.317703
Usage of this product signifies your acceptance of the Terms of Use.