[PPL-devel] Technical questions on how to extend a polyhedron

[giuseppe lipari]

Dear all,

we are using the PPL (C++ version) to model a parametric real-time 
scheduling problem.
At some point in our methodology, we obtain a region of space 
constrained by a C_Polyhedron that describes a subset of valid solutions 
for our problem.

Our problem has also this nice property: if X=(x_1, ..., x_n) is a 
vector contained in the C_Polyhedron, then any Y = (y_1, ...., y_n) with

    forall i 0<= y_i <= x_i,

is also a valid solution.

Therefore we would like to extend the C_Polyhedron to include all 
vectors   0<= Y <= X.

So, our questions are:

1) Is there any simple way of doing it in PPL?

In 2D we thought of the following simple strategy: add points (0,0) 
(x1,0) (0, x2) to the set of generators of the polyhedron, then minimize 
it.

2) Is this strategy correct?
3) How can we extend it to N dimension?

Thanks in advance for your kind response

Giuseppe Lipari
Laboratoire Spécification et Vérification,
Ecole Normale Supérieure de Cachan