PC7

n1n
n(n−1)/2
1
1
N P
u v w d(u, v)≤
d(u, w) + d(w, v)
•T
•H T
H∗c(T)T
H∗
c(H)H
2c(T)
(2 −)c(H∗)
G= (V, E)c(e)≥0
e∈E k v1, . . . , vk{v1, . . . , vk}G
F i 6=j{1, . . . , k}vivjG\F
F
F∗
F Gi[F]
viG\F FiF
Gi[F]Fivivjj6=i
vivjj6=i G \Fi
Eivivj
Ei
{v1, . . . , vk}
E
S={Si}1≤i≤mE Siw(Si)
J⊆ {1, . . . , m} ∪j∈JSj
EPj∈Jw(Sj)
N P
J
X|X|X\Y X Y

F← ∅ J← ∅
F6=E
c(Si) = w(Si)/|Si\F|i= 1, . . . , m
i c(Si)
F←F∪SiJ←J∪ {i}
J
(Ti)1≤i≤k
W0Si
Siw(Si)
|Si|≤W0 n
w(T1)
|T1|≤W0 n
x1, . . . , xnE F
TixjF
c(Ti)≤W0/(n−j+ 1)
HnHn= 1 + 1/2 + . . . + 1/n
n+ 1 E={1,2, . . . , n}Si={i}1≤i≤n Sn+1 =E
ε > 0
Hn/(1 + ε)
n(k, D)
X={x1, . . . , xn}d(xi, xj)
k D
Y k X xixj
Y d(xi, xj)≤D
d(xi, xj)
d(xi, xj)≤d(xi, x`) + d(x`, xj)i, j, `
D
k∗(k∗, D)
Y
xiY
D xi
2D
k∗
k∗
k
k D∗(k, D∗)
Y
k
Z={z1, . . . , zn}S={s1, . . . , sm}Z
k
k S Z
α < 2
k
(k, D)D= 1