1 Couverture par sommets

G= (V, E)w:V→Q+S⊆V
∀e∈E, ∃s∈S:s∈e
w
w
∃c > 0,∀v∈V:w(v) = c·deg(v)
{G= (V, E), w}w
w(V)≤2·OP T w(V) = Pv∈Vw(v)
p w p
G= (V, E)
w
t←0
G0←G
w0←w
Gt
Dt←u∈Vt:degt(u) = 0
pt←wtGt
St←u∈Vt:pt(u) = wt(u)
Gt+1 ←Gt\(Dt∪St)
wt+1 ←wt−pt
t←t= 1
C=
t−1
[
k=0
Sk

C
v∈C w(v)pk
v /∈C
pk(u)=0 u /∈Gt
C∗
{G= (V, E), w}
pi(C∩Gi)pi(C∗∩Gi)
C∩GiC∗∩GiGi
2.OP T