Jean Philippe,
> Jim,
>
> At 07:05 PM 12/31/2003 -0800, Jim Boyle wrote:
>
> >JP, so you state that both optimality and scalability are
> >requirements, yet you acknowledge that there will be trade-offs. I
> >believe it is important to prioritize the requirements, so as to best
> >guide the discussion on the solution.
>
> A few comments:
> - you seem to make the statement that optimal always means non scalable,
> something I disagree with. Of course, more optimal very likely means more
> expensive to compute, hence the trade-off I was referring to.
Whether optimality means scalability depends on the problem complexity.
E.g., for problems with log or (low) polynomial complexity optimality
need *not* mean non scalable; on the other hand, for NP-complete problems
optimality certainly *does* mean non-scalable.
> - moreover, the notion of scalability of a particular computation solution
> must be determined based upon specific criteria: implementation
efficiency,
> frequency at which the computation is triggered, computation time, ...
These are useful factors to consider, but we need to keep in mind
that no amount of implementation efficiency would provide an exact
(optimal) solution to an NP-complete problem in log or polynomial
time. (There are approximate algorithms that allow to solve NP-complete
problems in log or polynomial time, but these algorithms by no means
provide an optimal solution).