The following numbers are to be used in the making of the network tree. Based on the minimal spanning tree protocol these values will be assigned in a chronological order going from left to right and subsequently downwards in nature, the numbers are:
2, 5, 6, 11, 3, 3, 7, 7, 7, 4, 6, 9
7
5
4
6
9
7
7
3
3
11
6
2
G
F
H
E
D
C
B
A
Spanning Tree (Step One)
The above graphical representation is step one of the overall schematic the overall schematic that will be necessitated to be able to construct a successful spanning tree model. With the above graphical representation in place we can now start reducing nodes that may not be minimalistic and remove them from the overall model. The step two below provides a course correction for the network with the aim being that the smallest possible route is to be selected.
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7
5
4
6
9
7
7
3
6
2
G
F
H
E
D
C
B
A
Spanning Tree (Step Two)
5
4
7
3
3
6
2
G
F
H
E
D
C
B
A
Spanning Tree (Step Two)
The above final representative diagram showcases the minimum amount, in terms of network pathway, that would be required to completely adjoin every node to the other. This schematic will utilized the least number of resources while providing a pathway that fully connects all the given nodes in the network. Problem Set (9-33) For Bechtold construction to minimize the total length of wire to be used, they would have to employ a minimal spanning tree method upon which the shortest possible route would be determined between the constructed houses. Below is the general schematic which needs to be worked upon.
To resolve this network diagram we take an arbitrary node (in our case node 1) and then start solving the diagram based on the smallest subsequent value. From Node 1 the smallest is that leading to node three after which we have a tie between node (1 to 4) and (3 to 4). We take (node 1 to 4) because it then helps us to connect node 5 in the shortest possible manner as well. To resolve node 2 we just connect node (1 to 2) however we can’t proceed anywhere from node 2 so we return to node 3 which leads us to node 6 and then subsequently node 7 as well. The shortest next distance from Node 7 is node 9 which further prongs into an isolated node (node 9), a chain of node 10, 11 and 13 and finally concluding the network with 12 and 14 directly from node 9. The below schematic is the final representation of problem set 9-33.
3
Spanning Tree (Solved)
Problem Set (9-35)
The basic and most interesting parameter for the director is using 5 cables only that will provide the least expensive route for his network. Since we can arbitrarily start from anywhere in the network, we will proceed with node 1 as our starting point while the below graphs networked diagram would be utilized to the resolve this problem.
Based on the above diagram we will start from node 1 and move to node 3 which will branch off into node 2, node 3, and node 5 respectively. From node 5 we can go to Node 6 which we be the shortest route to Node 6 as any other route would either be from node 2 or node 3 itself which, from the above graph, are numerically higher than going from node 5. Also, the below schematic provides 5 cables that are necessary to route this network.
Below is the solved network schematic ranging from City 1 to City 16! To accommodate the best possible route, the shortest distance was calculated and then the below network drawing was mapped. It is essential to note that the minimal spanning tree method was used to resolve this problem.
The above diagram represents the shortest distance between City 1 up until city 16. However, if there is flooding in City 7 it would cut the main route and no cities would be accessible apart from city, 1, city 3 and city 4. On the other hand if City 8 is flooded then the route will remain active for all other cities apart from city 8 itself since there is only one prior connecting node to city 8 (city 4) and no cities are connect to it subsequently from that point onwards.
