Assignment is based on Discrete structure.

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Chapter

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Category :

Graph: Spanning Tree

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Algorithm

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$$Approach:

Kruskal algorithm

How can we leverage the Kruskal algorithm to determine a minimum spanning tree for the transportation networks linking Johor Bahru, Melaka, Selangor, and Kuala Lumpur, addressing issues of inefficiency and high construction costs?

Here's a suggested structure for presenting the MST analysis in this assignment

$1.$ Introduction:

Briefly introduce the problem of optimizing transportation networks between Johor Bahru, Melaka, Selangor, and Kuala Lumpur.

Explain the concept of graph theory and minimum spanning trees $($MSTs$)$ as tools for solving such problems.

State your chosen algorithm $($Kruskal$\text{'}$s algorithm$)$ and its purpose.

$2.$ Data and Graph Construction:

Present the distances or travel times between the cities in a table format.

Display both the complete weighted graph & Adjacent matrix $($with all possible edges$)$ and the MST graph for visual comparison. This highlights the process of identifying the most efficient connections.

Explain the rationale behind the MST$\text{'}$s structure, emphasizing its focus on minimizing overall travel time.

$3.$ Algorithm Implementation:

Outline the steps of Kruskal's algorithm in a clear and concise manner, ensuring understanding for readers unfamiliar with graph algorithms.

Demonstrate how the algorithm was applied to the specific data to arrive at the MST$.$

$4.$ MST Analysis:

Interpret the MST graph, highlighting the key connections and their implications for network design.

Discuss the total travel time achieved by the MST and its significance for optimization.

Explain the strategic omission of certain direct connections $($e$.$g$.,$ Johor Bahru $-$ Kuala Lumpur$)$ in favor of more efficient indirect paths.

$5.$ Conclusion and Recommendations:

Recap the main findings of the MST analysis, emphasizing its effectiveness in identifying the most cost$-$effective connections.

Discuss potential implications for network construction and planning based on the MST results.

Suggest further research avenues or extensions to the project, such as incorporating additional factors $($e$.$g$.,$ traffic patterns, construction costs$)$ into the model.