Question

In the network below, let us suppose that the link between nodes ‘k’ and ‘m’ has been failed. Using your knowledge of link-state routing, calculate the shortest path from node ‘i’ to node ‘j’ before failure and after failure. Also, mention the costs from node ‘i’ to node ‘j’ before failure and after failure.

[Hint = For example, the cost from node ‘i’ to node ‘r’ is 1 and the path is i-r]

m 4 n 5 r 1

Answer 1

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SOLUTION

Solution Dijkstra Algorithm Algorithm 1. S = . 2. Q = V[Source] 3. while Q! =0 (Q = Quene) u= extract Min (Q). s= s= {u}. for each ve Adjacent [u] & Not in Q. it a [v] . > d [u] +60. - d[v] =d[u]tw a [v] = uitzin When kto m pathenist. No ©

7 (Parent) Nil :> ☺ x Ę ç lable distance 04 - 32 xe & c.no

Queue 1. Si 2. Pop i and add adjacent verten and update in distance tableabore 4. Popr asr is min 5. [klm In 6 Popk 7. Pop n as n is minimum 8. [ ni 9. Pop j and add adjacent nodes not in queue 11. Now pop n. 12. klop 13. Up dating waits value in distance whose value less than table. So we got path shortes of è toj = 5.

REVER And path we trace from parent Parent of j in table is on Parent of m intable is k Parent of k is i (source) So path Shortest distance =i+Kym; = 5 So Now Similarity we calculate when path does not crist. from k tom. y od Now , Quere Table distance Parent Ni) 2. klo 3. For [knat 4. Then fork 5. Then for q 6. Then forn. 7. Thien for i and END. - For i toj a So distance =10 korost 3 en & eo con I = PATH = irq panj -

So we got that

when path from k to m exist

Shortest Distance = 5 and path = i -> k -> m -> j

when path from k to m does not exist

Shortest Distance = 10 and path = i -> r -> q -> p -> n -> j