Resolving the query inference problem using Steiner trees

Abstract

The query inference problem is to translate a sentence of a query language into an unambiguous representation of a query. A query is represented as an expression over a set of query trees. A metric is introduced for measuring the complexity of a query and also a proposal that a sentence be translated into the least complex query which "satisfies" the sentence. This method of query inference can be used to resolve ambiguous sentences and leads to easier formulation of sentences. l 349can be "executed" directly or translated into some logical expression (such as relational algebra or calculus). The query inference problem is uninteresting unless the QL provides some logical data independence. A measure of logical data independence can be achieved in a QL if tuple variables are implicitly bound to derived relations, rather than explicitly bound to specific relations. The relational QL without relations [15] is an example of such a language.Let A(t) be the set of attributes that appears with tuple variable t. We want a derived relation R(t) with a set of attributes A(t). There are several approaches to the computation of a derived relation (see [17, 201 for a general discussion). We review two universal relation approaches before introducing one of our own.One approach to the computation of R(t), given A(t), is to form a universal relation as the natural join of all the relations in the database and let R(t) be its projection onto A(t). (The relations can made to join completely by introducing tuples with null values.) This approach works well when the database scheme satisfies an acyclic join dependency [8].Maier and Ullman [16] demonstrate that when the database scheme is cyclic, the previous approach does not always assign an intuitive meaning to R(t). They explain how maximal objects can be used to give a more intuitive meaning to R(t). In their approach, an object is a computed relation representing a meaningful connection between all its attributes. A maximal object is an object contained in no other object. In the maximal object approach, R(t) is computed by selecting all maximal objects containing A(t), projecting them onto A(t), and taking the union. These maximal objects can be defined by the database administrator as in [17] or computed automatically using lossless joins [ 161.A problem with universal relational approaches is the unique role assumption among attributes, which can lead to a proliferation of attribute names [8]. This does not exist in the Entity-Relationship (ER) model because different roles between attributes are represented by different paths in the ER diagram. The maximal object approach has been adapted by Zhang and Mendelzon for the ER model [26]. They compute such objects automatically from the cardinalities of the relationships.In the maximal object approach, all maximal objects containing A(t) contribute to the computation of R(t) because there is no way to know which subset of maximal objects the user intended. We assume that a user wants only one object to be used in the computati...

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