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348 CHAPTER 8 NETWORK MODELS

Figure 8.4 GDA’s Network with Tentative Labels for Nodes 2 and 3

7
17
[15, 1]
5
2 6
6
15 4

3 6
[0, S] 4
2
1
10 5
4
3
[10, 1]

route to node 3 cannot be found. Accordingly, node 3 is permanently labelled with a
distance of 10km. Dark shading indicates that node 3 is a permanently labelled node
and the arrow indicates that node 3 will be used to start the next step of the labelling
process; the result of these steps is shown in Figure 8.5.
We now proceed by considering all nodes that are not permanently labelled and
that can be reached directly from node 3; these are nodes 2 and 5. Note that the
direct distance is 3km from node 3 to node 2 and it is 4km from node 3 to node 5.
Because node 3’s permanent label indicates that the shortest distance to node 3 is
10km, we see that we can reach node 2 in 10 + 3 ¼ 13km and node 5 in
10 + 4 ¼ 14km. So, the tentative label at node 2 is revised to [13, 3] to indicate
that we have now found a route from node 1 to node 2 that has a distance of 13kms
and passes through node 3. The tentative label for node 5 is set to [14, 3]. Figure 8.6
shows the network calculations up to this point.

Figure 8.5 GDA’s Network with Node 3 Identified as a Permanently Labelled Node

7
17
[15, 1]
5
2 6
6
15 4
3 6
[0, S] 4
2
1
10 4 5
3
[10, 1]

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