
The Power of Polyhedra 37
Here, every constraint saturates two vertices/rays and every vertex/ray sat-
urates two inequalities. This is also a nonredundant system. However the pos-
itivity constraint is also irredundant ... it is needed to support the presence
of the two rays. Without it, the two rays are not supported and appear mis-
takenly to be redundant.
Example 2.10 {x | x ≥ 1}
x>=1 1>=0
line(0,1) sat sat
vertex(1,2) sat
ray(1,0) sat
....
....
.
.
.
.
.
r
6
-
6
-
?
4
3
2
1
231
x
y
A halfplane.
2.3.5.2 Empty polyhedra
Example 2.11 An empty polyhedron: {x, y |1=0}
Empty Polyhedron, Dimension 2
Constraints ( 3 equalities, 0 inequalities )
x=0
y=0
1=0
Lines/Rays ( 0 lines, 0 rays ...