
The Power of Polyhedra 57
P (i + v)
XX
YY
Qi
D (Y)
Q
P
v
D
Pi
D (X)
i
(a)
Q (i + v)
D
P
Pi
Q
v
D (X)
(b)
D (Y)
Qi
i
Figure 2.14 Broadcast and reduction.
Broadcasts Broadcasts are created when there exists a vector v in Null(Q),
which is not in Null(P ). Refer to Figure 2.14a. If v is the vector separating
two points in D and v is in the null space of Q, then the two points in D
will map to the same point in D(Y ). If v is not in the null space of P , then
these two points will map to two distinct points in D(X). This means that
two or more values in X are dependent on a single value in Y and this is a
broadcast.
Reductions Refer to Figure 2.14b. If v is in the null space of ...