In this chapter, we learned about "weighted" graphs (graphs with numbers called "weights" on each of its edges), and we learned about two special types of weighted graphs:
Minimum Hamilton Circuit: a circuit which visits each vertex in a graph exactly once (returning to the starting vertex) and which has the smallest total weight
Minimum Spanning Tree: a subgraph of the original graph which is a tree, which includes all vertices in the original graph, and which has the smallest total weight
Please research and find an example of how one of these can be applied to solve a real-world problem and report your findings.
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One example of how the concept of Minimum Spanning Tree (MST) can be applied to solve a real-world problem is in the construction of telecommunication networks. Telecommunication companies often need to build a network infrastructure that connects multiple cities or locations, and they aim to minimize the cost of laying down the necessary cables.
By representing the cities or locations as vertices in a graph and the connections between them as edges with weights representing the cost of laying cables, finding the MST allows the telecommunication company to determine the most cost-effective way to connect all the locations.
For instance, let's consider a scenario where a telecommunication company needs to connect five cities. The distances between the cities and the cost of laying cables (weights) are as follows:
City A - City B: Distance = 100 km, Cost = $500
City A - City C: Distance = 150 km, Cost = $600
City B - City C: Distance = 200 km, Cost = $800
City B - City D: Distance = 300 km, Cost = $1000
City C - City D: Distance = 250 km, Cost = $900
City D - City E: Distance = 100 km, Cost = $400
By applying a MST algorithm, such as Kruskal's algorithm, the telecommunication company can determine the minimum cost of connecting all the cities. Suppose the resulting MST is formed by the edges:
City A - City B
City A - City C
City B - City D
City D - City E
The total cost of laying cables in this MST would be $2900, which provides the telecommunication company with the most efficient and cost-effective way to connect all the cities.
In summary, the application of the Minimum Spanning Tree concept allows telecommunication companies to optimize the connection of cities or locations in their network infrastructure, minimizing the costs associated with laying down communication cables.
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