Nested loop join

The naive algorithm that joins two relations $R$ and $S$ by making two nested loops:

  For each tuple in R as r do
     For each tuple in S as s do
        If r and s satisfy the join condition
           Then output the tuple <r,s> 

The algorithm runs in $O(|R||S|)$ I/Os, where $|R|$ and $|S|$ is the number of tuples contained in $R$ and $S$ respectively. Can easily be generalized to join any number of relaitons.