Computing full disjunctions

Abstract

Under either the OR-semantics or the weak semantics, the answer to a query over semistructured data consists of maximal rather than complete matchings, i.e., some query variables may be assigned null values. In the relational model, a similar effect is achieved by computing the full disjunction (rather than the natural join or equijoin) of the given relations. It is shown that under either the OR-semantics or the weak semantics, query evaluation has a polynomial-time complexity in the size of the query, the database and the result. It is also shown that the evaluation of full disjunctions is reducible to query evaluation under the weak semantics and hence can be done in polynomial time in the size of the input and the output. Complexity results are also given for two related problems. One is evaluating a projection of the full disjunction and the other is evaluating the set of all tuples in the full disjunction that are non-null on some given attributes. In the special case of γ-acyclic relation schemes, both problems have polynomial-time algorithms in the size of the input and the output. In the general case, such algorithms do not exist, assuming that P ≠ NP. Finally, it is shown that the weak semantics can generalize full disjunctions by allowing tuples to be joined according to general types of conditions, rather than just equalities among attributes.