(although modern databases may do something more complicated, I'm not sure)
Instead of n^2 operations it is more like m * ((n/m)^2) that can be evaluated in parallel across the m groups.
The simplest example of this is hash joins and equality filters. Keys that match on equality will also be grouped into the same hash bucket, reducing the search space. Keys that hash to different buckets will never be equal. The join is therefore the union of the cartesian product on each hash bucket, which requires fewer operations than filtering the cartesian product of the entire key set.
SQL does have set operations, and the Venn diagram treatment is much less terrible [though still not quite accurate] at explaining SQL set semantics.
The biggest flaw with the Venn diagram thing is that it doesn't capture the productive aspect of joins.
A inner join B on (some-condition) will produce ALL combinations of A records pasted to B records where some-condition holds.
The Venn diagram approach can't distinguish between a single A-pasted-to-B record and 100 thousand combinations of A-pasted-to-different-Bs. All it can say is that the resulting combinations consist of some set of A and B records.
Venn diagrams don't accurately describe the records resulting from a join at all. At best, they rule out records that can't occur.
So they're not so great as an explanatory device.
A [inner|left|right|outer|cross|natural|whatever] join B NEVER produces a result that is in either A or B. It produces something larger, that wasn't it A or B before.
It's like trying to describe the result of meiosis with a Venn diagram. It's the combinations that matter, and the combinations are not reflected in the Venn diagram.
The difference between the two is sometimes confusing for people, so I've always suggested that people learn one and stick with it, since you can accomplish the exact same thing with either.
http://skratchdot.github.io/list-tool/
Some of the algorithms aren't optimized (as to keep results in the order they were processed).
It was more of an experiment to play with web workers and responsive design.
Join Processing in Relational Databases, Priti Mishra and Margaret H. Eich, ACM Computing Surveys (CSUR) Surveys, Volume 24 Issue 1, March 1992, Pages 63 - 113
via http://www.allthingsdistributed.com/2013/04/join-processing-...
