Router 3s Perspective

To better understand the concept of the shortest-path tree, consider the network diagram presented in Figure 12-11. The simple network depicted is a small OSPF network. The administrator has enabled autocalculation of routing costs. It is important to note that the Ethernet installed between Routers 5 and 6 creates an alternate path for both networks and via Router 2. Therefore, it has an OSPF autocalculated cost of 10, whereas similar costs are not assigned to the other Ethernets.

The shortest-path tree for this network (illustrated in Figure 12-10) would vary from router to router. Figure 12-12, for example, presents this tree from the perspective of Router 3.

As is evident in Figure 12-12, the tree structure greatly facilitates the calculation of routing costs to any given destination. The root router (Router 3---, in this case) can quickly sum the costs associated with each interface encountered along a route to a given destination. From Router 3's perspective, routing costs to each of the networks are summed for you in Table 12-2. For destinations more than one hop away, the interface costs are summed in parentheses. This will enable you to trace the path through the network in Figure 12-12.

Table 12-2: Costs from Router 3 to Known Destinations


Hops Away

Cumulative Cost






65 (64 + 1)


128 (64 + 64)


129 (64 + 1 + 64)


1,833 (64 + 1 + 1768)


75 (64 + 1 + 10)

Figure 12-11: An OSPF network with routing costs.

Figure 12-12: Router 3's shortest-path tree.

In this example, there are two possible routes to network The one route contains fewer hops, but has a much higher cost due to the low-speed serial link between Routers 2 and 6. The alternate route has a higher hop count, but a much lower overall cost. In this case, OSPF would discard the higher-cost route and use the lower-cost route exclusively. If these two redundant routes had the same overall cost, OSPF would have maintained both routes as separate entries in its routing table and balanced the traffic as equally as possible between them.

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