Modules MAOA Projet 1 Cadre global du sujet

G= (V, A)a A
uv u a v P
(a1=u1u2, a2=u2u3, ..., al=ul−1ul)u1=ulP
W⊂V A(W)A
W G(W)=(W, A(W)
W
v∈V δ−(v)v δ−(v)
v d−(v) = |δ−(v)|d+(v) = |δ+(v)|
v

OiEi
Si
Ei
Vp={p1, ..., pn}Vo={o1, ..., om}
ojj∈ {1, ..., m}Ei
SiEi6=∅Si6=∅
PIN ⊂Vp
Vp\PIN |PIN |
V=Vp∪Vo
A oi∈Voi∈ {1, ..., m}
poip∈Eioip0
p0∈SiGC= (V, A)
p2PIN
p1o2o1
(o3, o1, o4, o8, o7, o5, o6)
o2o6
o2

PIN |PIN |= 9
o1
|PIN |= 7
G
Wo⊂VoH= (Wo∪Vp, A(Wo∪Vp))
m n M ≤n
oi|Ei| ≥ 1
|Si|>1|Ei|+|Si|< M
Ei|Ei|Si|Si|
EioioiSi

G= (V, A)V A
uv A u v G
P= (u0u1, u1u2, ..., uk−1uk)P k C
G u0=ukV(P)V(C)
W⊂V
A(W)W
(W, A(W)) W
(W, A(W)) G|W|
xi∀i∈V i
•
G= (V, A)u∈V
(PC)
Max X
u∈V
x(u)
u1= 1,
2≤ui≤n i 6= 1,
ui−uj+ 1 ≤n(2 −xi−xj)i6= 1, j 6= 1,
ui∈IR i,
0≤x(u)≤1∀u∈V
x(e)∀u∈V.
•
G= (V, A)u∈V
(PE)
Max X
u∈V
x(u)