The tree property is fundamental for query processing

One can partition the class of relational database schemas into tree schemas and cyclic schemas. In this paper we examine query processing implications of the partitioning; other areas impacted include dependency theory, schema design and graph theory.We consider a class of queries that compute the join of all relations in the database projected onto a prescribed set of attributes. We show that solving such queries (using the join, project and semijoin operators) is tantamount to creating an "embedded" tree schema which we call a tree projection. This lends further credibility to the pivotal nature of the tree/cyclic partitioning.Using the tree projection concept we analyze the problem of determining how many joins are needed to solve a query.