WORKED EXAMPLE 2.6
The distance matrix shown represents the lengths, in km, of gas pipelines that could be used to connect villages A, B, C , D , and E. Currently, the main gas supply only reaches as far as village A and it is required to connect the other villages to the main supply. B
C
D
E
A
−
5
2
7
4
B
5
−
6
−
7
C
2
6
−
D
7
−
7
E
4
7
6
PL E
A
7
6
−
3
3
−
a What total length of pipeline is needed if each of B, C , D and E needs to be directly connected to A?
b What total length of pipeline is needed if B, C , D and E can be connected to A via other villages (indirectly connected to A)? 18 km
b
14 km
BA + C A + DA + EA = 5 + 2 + 7 + 4 = 18
M
a
Use arcs in minimum spanning tree.
SA
WORK IT OUT 2.1
Find a minimum spanning tree for the network described by the distance matrix shown.
A
B
C
D
A
−
6
5
5
B
6
−
4
1
C
5
4
−
3
D
5
1
3
−
Which is the correct solution? Identify the errors made in the incorrect solutions. Solution 1
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