notes de cours d`algorithmique distribuée - Philippe GAMBETTE

O(n2)
O(nlog(n))
(C, →)C→C
S E = (γ1, γ2, . . .)∀i, γi→γi+1
S P ψ
L C
L
L P
P

L
S P
L
f:C→w w
γ→δ, f(γ)> f(δ)δ∈L
L
N
k∈N∗i σiJ0, k −1K
P0σ0=σn−1
Pi6=0 σi6=σi−1
P0
P0σ0=σn−1⇒σ0=σ0+ 1 mod k
Pi6=0 σi6=σi−1⇒σi=σi−1
σi
k P0
P0
Piσ0=σ1=. . . =σn−1
L
L
P0
F=P
i∈S
(N−i)S={i/i 6= 0 Pi}P0
P0F
P0FN(N−1)
2
F= 0 P0

pred
succ pred 6=succ
ψ p q pred(p) = q⇔succ(q) = p
p pq lpq
{pred, succ}pred succ
R
S
I
S
R
S
S
Sp∈ {S, R, I}
{Sp=I lpq =succ Sq=R lqp =pred} → Sp:= R lpq =succ
succ pred
{Sp=S lpq =succ Sq=R lqp =pred)} → Sp:= I
{Sp=R lpq =pred (Sq=S lqp =succ)} → Sp:= S
{Sp=Sq=S lpq =lqp =succ} → Sp:= R
{Sp=Sq=S lpq =lqp =succ} → Sp:= S

q p p
(1) −→ S I −→ R
(2) ←− R←− S←− I
(3) ¬−→ S−→ R−→ S
(4) −→ S←− S−→ R
(5) −→ I←− I←− S
q p →q p
(1) • × → • ×
(2) ו→•×
(3) ? • → =×
(4) • • → • ×
(5) × × → × •
L γ ∈L⇒ψ(γ)
p
γ R
γ
I S
I
S
N
N
N(N−1)
O(N2)
pref(p)
voisins ∪ ∅
p q
p
q wait
q p match
q p chain
p p
dead