Extension Joins

In proving that a set of relation schemes is a lossless decomposition of a set of attributes, it is sometimes possible to derive a sequence of extension joins whlich, upon execution, computes the join of the corresponding relations. Unlike natural join, any sequence of extension joins, which are really projections followed by joins, can be computed in polynomial time. The technique is effective in the important cases of decomposition into independent components and database schemes produced by Codd's third normal form algorithm.