# Re: Transitive Closure

From: Paul <paul_at_test.com>

Date: Fri, 14 May 2004 00:17:08 +0100

Message-ID: <OlToc.4051$NK4.344959_at_stones.force9.net>

> Is TClose a well defined operator? For a relation with 2 attributes we

Date: Fri, 14 May 2004 00:17:08 +0100

Message-ID: <OlToc.4051$NK4.344959_at_stones.force9.net>

Mikito Harakiri wrote:

> Paul <paul_at_test.com> wrote in message news:<%4noc.3394$NK4.266295@stones.force9.net>...

*>
*

>>But we can extend our DBMS by explicity including a "TClose" operator >>that takes a (two-columned) relation as its argument and returns a >>relation that is the transitive closure.

*>*> Is TClose a well defined operator? For a relation with 2 attributes we

*> could interpret it as Edges and look after TC of graph, but how is it**> defined when there is a third column? For one thing, that relation**> can't be interpreted as Edges anymore. Next, how is TClose defined for**> graphs with cycles?*Well, it would have to only be used for relations with two attributes that are of the same type, which does kind of break the symmetry of the other relational operators I must admit. Alternatively you could say it takes 3 arguments: one relation and two column names.

Wikipedia says: "...the transitive closure of a binary relation R on a set X is the smallest transitive relation on X that contains R."

So the word "smallest" should cover the case of graphs with cycles.

Paul. Received on Fri May 14 2004 - 01:17:08 CEST