Consider the network shown below and answer the following questions:

a$.(10\%)$ Show a spanning tree with Node $H$ as the root. Show the final routing table from Node A$\text{'}$s

perspective, with each row: $($destination: neighbor, distance$).$ Ignore the link cost here for spanning tree

and use the number of hops as the distance measure. $($Optional: those who are interested may look up

"minimum spanning tree" and discuss whether there is a "better" spanning tree for this network.$)$

b$.(15\%$ Use Dijkstra algorithm for Node A $($using the tabular format shown in class$)$ and find the routing

table: $($destination: neighbor, distance$).$ Take the link$-$cost into account for Parts $b$ and $c.$

c$.(15\%)$ Use Bellman$-$Ford algorithm for Node A: show the iterative updates of its Distance Table and

Distance Vector by considering the following distance vectors from Nodes B and H$,$ respectively. Show

the final routing table $($destination: neighbor, distance$)$ for Node A$.$

i$.$ B: $[A-2,C-1,E-5]$;$H$:$[A-10,E-2,G-1]$

ii$.$ B: $[A-2,C-1,D-2,E-4,H-7]$;$H$:$[A-10,B-7,C-5,E-2,F-2,G-1]$

iii. B: A$-2,$ C$-1,$ D$-2,$ E$-4,$ F$-3,$ G$-7,$ H$-6]$; H: A$-9,$ B$-6,$ C$-5,$ D$-6,$ E$-2,$ F$-2,$ G$-1]$

iv$.$ B: $[A-2,C-1,D-2,E-4,F-3,G-4,H-5]$;$H$:$[A-9,B-5,C-5,D-3,E-2,F-2,G-1]$

v$.$ B: A$-2,$ C$-1,$ D$-2,$ E$-4,$ F$-3,$ G$-4,$ H$-5]$; H: $[$A$-7,$ B$-5,$ C$-5,$ D$-3,$ E$-2,$ F$-2,$ G$-1]$

d$.(10\%)$ Use specific examples $($e$.$g$.,$ routes for traffic between A$-$F or B$-$H$)$ to discuss the differences

between the routes found in Parts a$,$ b$,$ and c$.$ Also comment on the information needed and computational

complexity for each of the three approaches.