Sequenced subset operators: definition and implementation

Difference, intersection, semi join and anti-semi-join may be considered binary subset operators, in that they all return a subset of their left-hand argument. These operators are useful for implementing SQL's EXCEPT, INTERSECT, NOT IN and NOT EXISTS, distributed queries and referential integrity. Difference-all and intersection-all operate on multi-sets and track the number of duplicates in both argument relations; they are used to implement SQL's EXCEPT ALL and INTERSECT ALL. Their temporally sequenced analogues, which effectively apply the subset operator at each point in time, are needed for implementing these constructs in temporal databases. These SQL expressions are complex; most necessitate at least a three-way join, with nested NOT EXISTS clauses. We consider how to implement these operators directly in a DBMS. These operators are interesting in that they can fragment the left-hand validity periods (sequenced difference-all also fragments the right-hand periods) and thus introduce memory complications found neither in their non-temporal counterparts nor in temporal joins and semijoins. We introduce novel algorithms for implementing these operators by ordering the computation so that fragments need not be retained in main memory. We evaluate these algorithms and demonstrate that they are no more expensive than a single conventional join.