Fiche TD: Algorithmes gloutons

{x1, . . . , xn}
p1,· · · , pn
v1,· · · , vn
c
c n
pivi
{x1, . . . , xn}xi
((di, fi))n
i=1, di< fidifii
aff : [1..n]→[1..p], p ≤n i

aff(i) = aff(j)i6=j]di, fi[∩]dj, fj[= ∅
card(aff([1..n]))
n
eisi
i
i
e1, e2(e2, e1)
e2c∗s2e1c∗(s2+s1)c
eσ(1), . . . , eσ(n)
M=c∗1/n ∗
n
X
j=1
(
j
X
k=1
sσ(k))
(e2, e1)
1/2∗c∗(s2+ (s2+s1)) c∗(s2+s1/2)
n
s1, s2, .., sn
σ(1), .., σ(n)M=c∗1/n∗Pn
j=1(Pj
k=1 sσ(k))
n= 3, s1= 12; s2= 26; s3= 19
i fiPn
ifi=
1
M=c∗
n
X
j=1
(fσ(j)∗
j
X
k=1
sσ(k))
(e2, e1)
c∗(f2∗s2+f1∗(s2+s1)) c(s2+f1∗s1)
si
fi
p n
plac1, ..., placp
dem1, ..., demn

n p
plac1, ..., placp
dem1, ..., demn
aff : [1..n]→[1..p]
aff(i)>=demi1≤i≤n
Card{i/aff(i) = j}<=placj1≤j≤p
p= 3 n= 6 2,1,3,2,2,3
demi< demjaffi<=affj
p= 3 n= 6 2,1,1,2,1,1
aff(1) = 2, aff(2) = 1, aff(3) = 1, aff(4) = 2, aff(5) = 3, aff(6) = 3
4 5
p= 3 n= 6 2,2,1,3,1,1
aff(i)−dem(i)
Pi=n
i=1 (aff(i)−demi)
p= 3 n= 6 2,1,1,2,1,1
aff(1) = 3, aff(2) = 1, aff(3) = 1, aff(4) = 3, aff(5) = 2, aff(6) = 1
(3 −2) + (1 −1) + (1 −1) + (2 −1) + (2 −1) + (1 −1) 3
n i = 1, . . . , n
di
t= 0 i ti
fi
ti> fi
maxi en retard(ti−fi)
4d1= 2, d2= 1, d3= 4, d4= 2 f1= 2, f2= 3, f3= 5, f4= 4
1,3,2,4,5 1,3,4,2 6

pi
Σn
i=1piti
d1= 2, d2= 1, d3= 4, d4= 2
p1= 1, p2= 1, p3= 3, p4= 2
1,2,3,4t1= 2, t2= 3, t3= 7, t4= 9
44
1,3,4,2
pi
d
Pi/ti>d pi
pi/di