If Q defined in (18) is £, then allocating functions l0k and l0jm
are the
same. So,
Pm
t¼1 ðzl0jt zl0jt1Þ ¼ 0. Suppose that Q –£. Allocating
functions l0k : N ! S [ fkg and l : N ! S [ fkg are different just in
the allocation of node k. Also, the allocating functions
l0jt : N ! S [ fkg and l0jt1
: N ! S [ fkg are just different in the allocation
of non-hub node jt which changes from l0jt1
to l0jt
. Thus,
suppose that