Lecture Notes in Computer Science 4917

296 R. Levin, I. Newman, and G. Haber
Where cp (o)
is a non negative vector of coefficients. Such functions are monotone
with the absolute amount of change for each edge/ vertex and are referred as weighted
l1 costs. Such functions give the ability, by chosing the right weights, to prefer
changes to some edges than to others (e.g due to some a-priory knowledge of the
reliability of the measurements at different sites). We can, however, do a bit more.
Weighted l1 costs do not distinguish between increasing and decreasing the flow at a
site. It might be important for some edges to charge more for decreasing the flow than
for increasing it (again, due to some prior knowledge on the flow). Thus we define:
∑
o∈V
∪E
( Δ(
o)
) = cp(
o Δ)
⋅ Δ(
o)
∑
cos t ( Δ)
= cost
,
(3)
o∈V
∪E
Where the coefficient cp(o,Δ) = k + (o) if Δ>0 and cp(o,Δ) = k - (o) if Δ