An incremental algorithm for computing ranked full disjunctions

The full disjunction is a variation of the join operator that maximally combines tuples from connected relations, while preserving all information in the relations. The full disjunction can be seen as a natural extension of the binary outerjoin operator to an arbitrary number of relations and is a useful operator for information integration. This paper presents the algorithm IncrementalFD for computing the full disjunction of a set of relations. IncrementalFD improves upon previous algorithms for computing the full disjunction in four ways. First, it has a lower total runtime when computing the full result and a lower runtime when computing only k tuples of the result, for any constant k. Second, for a natural class of ranking functions, IncrementalFD can be adapted to return tuples in ranking order. Third, a variation of IncrementalFD can be used to return approximate full disjunctions (which contain maximal approximately join consistent tuples). Fourth, IncrementalFD can be adapted to have a block-based execution, instead of a tuple-based execution.