BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI - Universitatea ...

c) Calculate values
(14)
⎧V
⎪
⎪
⎪V
⎪
⎪V
⎪
⎪
⎨V
⎪
⎪V
⎪
⎪
⎪V
⎪
⎪V
⎩
2
1
2
2
2
3
2
4
2
5
2
6
2
7
= min
= min
= min
= min
= min
= min
= 0
Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 2, 2010 211
2
V i for i = 1, ..., 7 (j = 1, ..., 7)
j≠1
j≠
2
j≠
3
j≠
4
j≠
5
j≠
6
1
1 1
1
( V j + m1
j ) = min(
V2
+ m12,
V3
+ m13,...,
V7
+ m17
)
1
1 1
1
( V j + m2
j ) = min(
V1
+ m21,
V3
+ m23,...,
V7
+ m27
)
1
1 1
1
( V j + m3
j ) = min(
V1
+ m31,
V2
+ m12,...,
V7
+ m37
)
1
1 1
1
( V j + m4
j ) = min(
V1
+ m41,
V2
+ m42,...,
V7
+ m47
)
1
1 1
1
( V j + m5
j ) = min(
V1
+ m51,
V2
+ m52,...,
V7
+ m57
)
1
1 1
1
( V + m ) = min(
V + m , V + m ,..., V + m )
j
6 j
d) To calculate the values corresponding to column
..., 7), an analogue, finally are obtained (15).
2
2
i
3
i
1
61
2
62
7
67
= 197
= 153
= 153
= 61 .
= 92
= 82
3
V i for i = 1, ..., 7 (j = 1,
Since V = V (i = 1, ..., 7), algorithm stops and the road is the minimum of
3
V1
=V1
= 197 . This value is reached on the way (1, 2, 6, 7), thus resulting in
optimal route of adduction as: S1, A, C, and L. To resolve this problem the
computer program BEL_KAL was used.
(15)
⎧V
⎪
⎪
⎪V
⎪
⎪V
⎪
⎪
⎨V
⎪
⎪V
⎪
⎪
⎪V
⎪
⎪V
⎩
3
1
3
2
3
3
3
4
3
5
3
6
3
7
= min
= min
= min
= min
= min
= min
= 0
j≠1
j≠
2
j≠3
j≠
4
j≠5
j≠
6
2 ( V j + m1
j )
2 ( V j + m2
j )
2 ( V j + m3
j )
2 ( V j + m4
j )
2 ( V j + m5
j )
2 ( V + m )
j
6 j
= 197
= 153
= 153
= 61 .
= 92
= 82