non-equi self-join optimization - Mailing list pgsql-sql

I have a table of names with two subsets of entities. I want to find
those names from set 1 that are substrings of names from set 2 from the
same table. Basically the pared down query I want is something like
this:
select t1.myname, t2.myname  from mytable t1     inner join mytable t2      on position (t1.myname in t2.myname) > 0
wheret1.flag = 1    and t2.flag = 2   
;

I have gone through a few variations on the theme, but none perform too
well. Any advice on the best way to optimize a query like this would be
appreciated.

Thanks!

George