Quando o nó mais distante do nó
x
{\displaystyle \ x}
x
{\displaystyle \ x}
localização com o menor valor possível de
M
V
V
{\displaystyle \ MVV}
Francis, 1992, p. 431-440 ):
M
V
V
(
x
)
=
min
{
M
V
V
(
i
)
}
{\displaystyle \ MVV(x)=\min {\big \{}MVV(i){\big \}}}
M
V
V
(
i
)
=
max
{
d
(
i
,
j
)
}
{\displaystyle \ MVV(i)=\max {\big \{}d(i,j){\big \}}}
matriz das distâncias mais curtas entre todos os pares de nós da Figura 9.12.2.3.1 é:
Figura 9.12.2.3.1 Exemplo de rede cíclica
D
=
[
0
3
5
4
6
0
2
2
7
2
0
3
4
5
3
0
]
{\displaystyle D={\begin{bmatrix}0&3&5&4\\6&0&2&2\\7&2&0&3\\4&5&3&0\end{bmatrix}}}
M
V
V
(
1
)
=
max
{
0
,
3
,
5
,
4
}
=
5
{\displaystyle \ MVV(1)=\max {\big \{}0,3,5,4{\big \}}=5}
M
V
V
(
2
)
=
max
{
6
,
0
,
2
,
2
}
=
6
{\displaystyle \ MVV(2)=\max {\big \{}6,0,2,2{\big \}}=6}
M
V
V
(
3
)
=
max
{
7
,
2
,
0
,
3
}
=
7
{\displaystyle \ MVV(3)=\max {\big \{}7,2,0,3{\big \}}=7}
M
V
V
(
4
)
=
max
{
4
,
5
,
3
,
0
}
=
5
{\displaystyle \ MVV(4)=\max {\big \{}4,5,3,0{\big \}}=5}
min
M
V
V
(
i
)
=
min
{
5
,
6
,
7
,
5
}
=
5
{\displaystyle \ \min MVV(i)=\min {\big \{}5,6,7,5{\big \}}=5}
Localização Central Geral
editar
Qualquer nó
x
{\displaystyle \ x}
M
V
A
(
x
)
{\displaystyle \ MVA(x)}
M
V
A
(
x
(
=
min
{
M
A
V
(
i
)
}
{\displaystyle \ MVA(x(=\min {\big \{}MAV(i){\big \}}}
M
V
A
(
i
)
=
max
d
′
(
i
,
(
r
,
s
)
)
{\displaystyle \ MVA(i)=\max d'(i,(r,s))}
D
′
{\displaystyle \ D'}
D
′
=
[
3
5
4
5
5
6
9
12
6
2
2
3
,
5
10
12
7
4
2
3
7
7
4
9
5
3
]
{\displaystyle D'={\begin{bmatrix}3&5&4&5&5&6\\9&12&6&2&2&3,5\\10&12&7&4&2&3\\7&7&4&9&5&3\end{bmatrix}}}
M
V
A
(
1
)
=
max
{
3
;
5
;
4
;
5
;
5
;
6
}
=
6
{\displaystyle \ MVA(1)=\max {\big \{}3;5;4;5;5;6{\big \}}=6}
M
V
A
(
2
)
=
max
{
9
;
12
;
6
;
2
;
2
;
3
,
5
}
=
12
{\displaystyle \ MVA(2)=\max {\big \{}9;12;6;2;2;3,5{\big \}}=12}
M
V
A
(
3
)
=
max
{
10
;
12
;
7
;
4
;
2
;
3
}
=
12
{\displaystyle \ MVA(3)=\max {\big \{}10;12;7;4;2;3{\big \}}=12}
M
V
A
(
4
)
=
max
{
7
;
7
;
4
;
9
;
5
;
3
}
=
9
{\displaystyle \ MVA(4)=\max {\big \{}7;7;4;9;5;3{\big \}}=9}
min
M
V
A
(
i
)
=
min
{
6
;
12
;
12
;
9
}
=
6
=
M
V
A
(
1
)
{\displaystyle \ \min MVA(i)=\min {\big \{}6;12;12;9{\big \}}=6=MVA(1)}
Distância Ponto-Nó
f
{\displaystyle \ f}
(
r
,
s
)
{\displaystyle \ (r,s)}
j
{\displaystyle \ j}
d
(
f
−
(
r
,
s
)
,
j
)
{\displaystyle \ d(f-(r,s),j)}
(
r
,
s
)
{\displaystyle \ (r,s)}
d
(
f
−
(
r
,
s
)
,
j
)
{\displaystyle \ d(f-(r,s),j)}
d
(
f
−
(
r
,
s
)
,
j
)
=
min
{
f
a
(
r
,
j
)
+
d
(
r
,
j
)
,
(
1
−
f
)
a
(
r
,
s
)
+
d
(
s
,
j
)
}
{\displaystyle \ d(f-(r,s),j)=\min {\big \{}fa(r,j)+d(r,j),(1-f)a(r,s)+d(s,j){\big \}}}
(
r
,
s
)
{\displaystyle \ (r,s)}
d
(
f
−
(
r
,
s
)
)
,
j
)
=
(
1
−
f
)
a
(
r
,
s
)
+
d
(
s
,
j
)
{\displaystyle \ d(f-(r,s)),j)=(1-f)a(r,s)+d(s,j)}
Localização Central Absoluta
editar
Um ponto qualquer cujo nó mais distante está o mais próximo possível é um centro absoluto, ou seja, o centro absoluto é o ponto
d
(
f
−
(
r
,
s
)
{\displaystyle \ d(f-(r,s)}
M
P
V
(
f
−
(
r
,
s
)
)
=
min
M
P
V
(
f
−
(
t
,
u
)
)
{\displaystyle \ MPV(f-(r,s))=\min MPV(f-(t,u))}
f
−
(
t
,
u
)
∈
P
{\displaystyle \ f-(t,u)\in P}
M
P
V
(
f
−
(
t
,
u
)
)
=
max
{
f
(
f
−
(
t
,
u
)
,
j
}
{\displaystyle \ MPV(f-(t,u))=\max {\big \{}f(f-(t,u),j{\big \}}}
Localização Central Absoluta Geral
editar
Qualquer ponto
x
{\displaystyle \ x}
Um centro absoluto geral é um ponto
f
−
(
r
,
s
)
{\displaystyle \ f-(r,s)}
M
P
A
(
f
−
(
r
,
s
)
)
=
min
{
M
P
A
(
f
−
(
t
,
u
)
)
}
{\displaystyle \ MPA(f-(r,s))=\min {\big \{}MPA(f-(t,u)){\big \}}}
f
−
(
t
,
u
)
∈
P
{\displaystyle \ f-(t,u)\in P}
M
P
A
(
f
−
(
t
,
u
)
)
=
max
{
d
′
(
f
−
(
t
,
u
)
,
(
v
,
w
)
)
}
{\displaystyle \ MPA(f-(t,u))=\max {\big \{}d'(f-(t,u),(v,w)){\big \}}}
