Algorithm Question

[John Machin]

Andrew McLean wrote:
> Carl Banks wrote:
> > Andrew McLean wrote:
> >> I have a list of strings, A. I want to find a set of strings B such that
> >> for any "a in A" there exists "b in B" such that b is a sub-string of a.
> >
> > B=A?
> >
> >> But I also want to minimise T = sum_j t_j where
> >> t_j = count of the number of elements in A which have b[j] as a sub-string
> >
> > If there not elements in A that are substrings of any other element in
> > A, and if B=A, then t_j would be 1 for all j.  Which means B=A would be
> > optimal (since elements of B have to be substring of at least one
> > element in A).  It looks like the B={set of all elements in A that are
> > not a substring of any other element in A} is the generally optimal
> > solution.
> >
> > I suspect you mistyped or omitted something--problem is underspecified
> > at best.
>
> You are quite right. I was trying to generalise my real problem and
> missed out a constraint. I also want to keep length(B) small.
> Unfortunately, I'm a bit unsure about the relative importance of T and
> length(B), which makes the problem rather ill defined. I'll have to give
> this a bit more thought....

A quick silly question: what is the problem that you are trying to
solve?