This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Using Constraints for Efficient Query Processing in Nondeterministic Databases
December 1995 (vol. 7 no. 6)
pp. 850-864

Abstract—Nondeterministic databases store disjunctive data using OR-objects. For example, data such as “Part#1 is implementable using Nickel or Cobalt” is stored as Implement(Part#1, o1) where Dom(o1) ={Nickel, Cobalt}; is the domain of the OR-object o1. A possible world of a database is obtained by replacing every OR-object by a member from its domain, and it is said to be conforming if it satisfies all the FDs (functional dependencies) associated with the database. A database D is said to fully incorporate a set ${\cal F}$ of FDs if every possible world of D is conforming. This paper studies the problem of preprocessing databases to achieve full incorporation, and also the problem of incrementally maintaining a database fully incorporated under insertions and deletions.

We first define a certain property called goodness of a class ${\cal D}$ of databases for a set ${\cal F}$ of FDs; goodness can be tested efficiently and enforced easily at schema design time.

For any class ${\cal D}$ of databases that is good for ${\cal F}$, we present: 1) a quadratic time algorithm for fully incorporating ${\cal F}$, 2) efficient algorithms for maintaining full incorporation under updates, and 3) lower-bounds for the algorithms of 1) and 2). Next, we show that, for classes of databases that are not good, the problem of full incorporation is, in general, coNP-complete. We also examine the complexity when OR-objects are restricted to have no more than two members, and obtain some interesting tractable algorithms, and intractability results.

[1] C. Beeri and M. Vardi,“A proof procedure for data dependencies,” J. ACM, vol. 31, no. 4, pp. 718-724, Oct. 1984.
[2] J. Biskup,“A formal approach to null values in database relations,” Advances in Database Theory, Gallaire and Minker, eds., pp. 299-341.New York: Computer Science Publications, 1981.
[3] E. Codd,“Extending the database relational model to capture more meaning,” ACM Trans. Database Systems, vol. 4, no. 4, pp. 397-434, 1979.
[4] M. Dincbas,H. Simonis,, and P. Van Hentenryck,“Solving a cutting-stock problem in constraint logic programming,” Proc. Fifth Int’l Conf. Logic Programming, 1988.
[5] M. Dincbas,H. Simonis,, and P. Van Hentenryck,“Solving the car sequencing problem in constraint logic programming,” Proc. European Conf. Artificial Intelligence, 1988.
[6] D. Dobkin and R. Lipton,“On the complexity of computations under varying set of primitives,” J. Computer and Systems Sciences, vol. 18, no. 86, 1979.
[7] S. Even,A. Itai,, and A. Shamir,“On the complexity of timetable and multicommodity flow problems,” SIAM J. Computing, vol. 5, no. 4, Dec. 1976.
[8] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness.New York: W.H. Freeman, 1979.
[9] J. Grant,“Null values in a relational data base,” Information Processing Letters, vol. 6, no. 5, pp. 156-157, 1977.
[10] T. Imielinski, “Abstraction in Query Processing,” J. ACM, vol. 38, pp. 534-558, 1991.
[11] T. Imielinski,“Incomplete deductive databases,” Annals of Mathematics and Artificial Intelligence, vol. 3, pp. 259-294, 1991.
[12] T. Imielinski and W. Lipski Jr.,“Incomplete information in relational databases,” J. ACM, vol. 31, no. 4, pp. 761-791, 1984.
[13] T. Imielinski,R. van der Meyden,, and K. Vadaparty,“Complexity tailored design—a new methodology for databases withincomplete information,” J. Computer and System Sciences, vol. 53, no. 3, pp. 405-432, 1995.
[14] T. Imielinski,S. Naqvi,, and K. Vadaparty,“Incomplete objects—A data model for design and planning applications,” Proc. ACM SIGMOD Conf., pp. 288-297, 1991.
[15] T. Imielinski,S. Naqvi,, and K. Vadaparty,“Querying designing and planning databases,” Proc. Second Int’l Conf. Deductive object-Oriented Databases,Munich, Dec. 1991.
[16] T. Imielinski and K. Vadaparty,“Complexity of query processing in databases with OR-objects,” Proc. ACM PODS Conf., pp. 51-65, 1989.
[17] L. Libkin and L. Wong,“Semantic representations and query languages for or-sets,” Proc. ACM PODS Conf. , pp. 37-48, 1993.
[18] W. Lipski,“On semantic issue connected with incomplete information systems,” ACM Trans. Database Systems, vol. 4, no. 3, pp. 262-296, 1979.
[19] W. Lipski Jr.,“On databases with incomplete information,” J. ACM, vol. 28, no. 1, pp. 41-70, 1981.
[20] J. Lobo, J. Minker, and A. Rajasekar, Foundations of Disjunctive Logic Programming. Cambridge, Mass.: MIT Press, 1992.
[21] D. Maier,“Discarding the universal INstance assumption: Preliminary results,” XP1 Workshop Relations Database Theory, June-July 1980.
[22] D. Maier,The Theory of Relational Databases, vol. 1. Computer Science Press, 1983.
[23] J. Minker and A. Rajasekar, “A Fixpoint Semantics for Disjunctive Logic Programming,” J. Logic Programming, vol. 9, no. 1, pp. 45-74, 1990.
[24] A. Ola and G. Ozsoyoglu,“Incomplete relational database models based on intervals,” IEEE Trans. Knowledge and Data Engineering, vol. 5, no. 2, pp. 293-308, 1993.
[25] F.P. Preparata and M.I. Shamos, Computational Geometry. Springer-Verlag, 1985.
[26] E.M. Reingold,“On the optimality of some set algorithms,” J. ACM, vol. 19, pp. 649-659, 1972.
[27] R. Reiter,“Toward a logical reconstruction of relational database theory,” On Conceptual Modeling, M.L. Brodie and J.W. Schmit, eds. Springer-Verlag, 1984.
[28] R. Reiter,“A sound and sometimes complete query evaluation algorithm forrelational databases with null values,” J. ACM, vol. 33, no. 2, pp. 349-370, 1986.
[29] G.J. Smith,“Determining the requirements for the sub-assembly module,” Technical Report TM-OPT-08617,Bellcore, Morristown, N.J. Mar. 1991.
[30] J. Ullman, Principles of Database and Knowledge-Base Systems, vol. 1. Computer Science Press, 1988.
[31] P. van Hentenryck, Constraint Satisfaction in Logic Programming, Logic Programming Series, MIT Press, Cambridge, Mass., 1989.
[32] M. Vardi,“Querying logical databases,” J. Computer and System Sciences, vol. 33, pp. 142-160, 1986.
[33] Y. Vassiliou,“Null values in database management: A denotational semantics approach,” Proc. ACM SIGMOD Conf., pp. 162-169, 1979.
[34] A. Walker,“Time and space in a lattice of universal relations with blankentries,” XP1 Workshop Relational Database Theory, June-July 1980.
[35] L.Y. Yuan and D.A. Chiang, “A Sound and Complete Query Evaluation Algorithm for Relational Databases with Disjunctive Information,” Proc. Eight Symp. Principles of Database Systems, pp. 66-74, 1989.

Index Terms:
Nondeterministic data, constraints, efficiency of query processing.
Citation:
Kumar Vadaparty, Shamim Naqvi, "Using Constraints for Efficient Query Processing in Nondeterministic Databases," IEEE Transactions on Knowledge and Data Engineering, vol. 7, no. 6, pp. 850-864, Dec. 1995, doi:10.1109/69.476493
Usage of this product signifies your acceptance of the Terms of Use.