The tree projection theorem and relational query processing

AbstractThe class of relational database schemas can be partitioned into two subclasses: tree schemas and cyclic schemas. This partitioning has consequences in several areas of database theory, including query processing, dependency theory, and schema design. Query processing consequences of the partitioning are examined. Queries, called natural join queries, that compute the natural join of all relations in the database projected onto a prescribed set of attributes are considered. Also programs that solve natural join queries by applying joins, semijoins, and projections in some order are considered. It is shown that if such a program solves a natural join query then it must create an “embedded” tree schema, called a tree projection. Conversely, if a program creates a tree projection then the program augmented with a small number of semijoins solves the query. Thus, forming a tree projection is the crux of the query processing problem for natural join queries