Interactive end-of-chapter exercises


Dijkstra's Link State Algorithm - Advanced

Consider the incomplete 6-node network shown below, with the given link costs.

Consider the completed table below, which calculates the shortest distance to all nodes from U:
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|    Node     |    Shortest distance from U    |    Previous Node   |
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       U                                0                                     n/a   
       W                               1                                     U   
       X                                2                                     W   
       Y                                2                                     W   
       V                                3                                     W   
       Z                                3                                     W   
================================================



Question List


1. For link X, what is the cost associated with this link? If the answer can't be determined given the information, respond with 'n/a'

2. For link Y, what is the cost associated with this link? If the answer can't be determined given the information, respond with 'n/a'




Solution


1. The prior node in the path to X is W, and we know the shortest distance of both X (2) and W (1), so 2 - 1 = 1 which is X.

2. The prior node in the path to V is W, and we know the shortest distance of both V (3) and W (1), so 3 - 1 = 2 which is Y.



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We greatly appreciate the work of John Broderick (UMass '21) in helping to develop these interactive problems.

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