Consider the following network. With the indicated link costs, use Dijkstra’s shortest-path algorithm to compute the shortest path from x to all network nodes. Show how the algorithm works by computing a table similar to Table 4.3.

Question

Answer 1

Dijkstra’s Algorithm:

• Dijkstra’s algorithm is a Link-state algorithm which computes the least-cost path from one node to all other nodes in the network.

• Dijkstra’s algorithm is iterative.

• The least-cost paths are known to k destination nodes after the  iteration of the algorithm. These k paths will have the k smallest costs among the least-cost paths to all destination nodes.

The following terms are used in the algorithm:

D(v) = least cost of the path from the source to the destination for the node v.

p(v) = previous node along the current path with least cost from source to node v.

N’ = subset of nodes.

The following table represents the computation of shortest path from source x to all the nodes in the network is as follows:

Therefore, the following are shortest paths from x along with their costs: t: xvt = 7; u: xvu = 6; v: xv = 3; w: xw = 6; y: xy = 6; z: xz = 8

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Comments

Can you provide the table for from t to all other nodes and from u to all other nodes?