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<p><it>Abstract</it>—Nondeterministic databases store disjunctive data using OR-objects. For example, data such as “Part#1 is implementable using Nickel or Cobalt” is stored as <it>Implement</it>(<it>Part</it>#1, <it>o</it><sub>1</sub>) where <it>Dom</it>(<it>o</it><sub>1</sub>) ={<it>Nickel</it>, <it>Cobalt</it>}; is the domain of the OR-object <it>o</it><sub>1</sub>. 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 <it>conforming</it> if it satisfies all the FDs (functional dependencies) associated with the database. A database <it>D</it> is said to <it>fully incorporate</it> a set <math><tmath>${\cal F}$</tmath></math> of FDs if every possible world of <it>D</it> 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.</p><p>We first define a certain property called <it>goodness</it> of a class <math><tmath>${\cal D}$</tmath></math> of databases for a set <math><tmath>${\cal F}$</tmath></math> of FDs; goodness can be tested efficiently and enforced easily at schema design time.</p><p>For any class <math><tmath>${\cal D}$</tmath></math> of databases that is good for <math><tmath>${\cal F}$</tmath></math>, we present: 1) a quadratic time algorithm for fully incorporating <math><tmath>${\cal F}$</tmath></math>, 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 <it>not</it> 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.</p>
Nondeterministic data, constraints, efficiency of query processing.

K. Vadaparty and S. Naqvi, "Using Constraints for Efficient Query Processing in Nondeterministic Databases," in IEEE Transactions on Knowledge & Data Engineering, vol. 7, no. , pp. 850-864, 1995.
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