Abstract: An equivalence rule having the multiset version of the relational algebraic theta-semijoin operator is used in effectuating Constraint Magic rewriting on a computer programming language query having non-equality, as well as equality, predicates. In particular, the rule effectuates Constraint Magic rewriting for a single join. When applied repeatedly on a sequence of joins, Constraint Magic rewriting is effectuated for a single block query. The rule may be used to generate relational algebraic expressions to optimize or determine the equivalency of queries. Cost estimates for alternative ways of evaluating a complex query can be efficiently computed. Based on these computed cost estimates, the least costly implementation of a complex query is determined.

Abstract: A collection of equivalence rules involving the multiset version of the relational algebraic theta-semijoin operator is used to generate relational algebraic expressions equivalent to a computer programming language query. These expressions may be employed as a search space which is utilized by, for example, optimizing software or software that determines the equivalency of queries. Cost formulas for the multiset version of the theta-semijoin operator may be used in computing cost estimates for the generated expressions. Based on these computed cost estimates, the least costly implementation of a complex query is determined. Thus, queries are cost-based optimized on both a local and global basis by use of the relational algebraic theta-semijoin operator.