Dijkstra's Algorithm Used for Route Optimization Assignment

Assignment Task

Introduction

In real life, the application of the shortest path is enormous. For example, in map software or a navigation system, It involves the problem of determining the shortest path from one location to another, and the path with the lowest cost is the shortest route. In certain circumstances finding shortest paths between given nodes may be achieved at a huge cost especially where time and efforts are of significant consideration, such cases are the basic consideration in this study [1]. In terms of transportation management and engineering design, for example, the arrangement of various process routes, the placement of power grids and pipe networks, route acquisition in electric maps, and so on, the shortest path issue is frequently involved. There are numerous shortest path algorithms, and the theory and algorithm process of these algorithms vary, making them suitable for a variety of problems. The shortest path problem is a computerised by graphic searching algorithm problem that identifies the optimal route with the lowest costs from the starting point to the target point. The main objective is to evaluate the Dijkstra’s Algorithm, Floyd-Warshall Algorithm and Bellman-Ford Algorithm, in solving the shortest path problem.

Bellman-Ford Algorithm

Bellman-Ford algorithm was designed to work for the negative edges and negative weight cycles. When discussing a directed graph, there may be a condition that can be taken into account in which negative weight edges may exist from the source node to all other nodes (G). Imagine that some of the edges of the directed graph (G) carry a negative weight from the source node to every other node. When we encounter a circumstance where some edges of the directed graph (G) may have negative weights from source node to all other nodes, the Bellman-Ford algorithm was used to determine the shortest distance or the optimal path. Dijkstra's Algorithm thus makes it challenging to solve graphs with negative edge weights. Although Bellman-approach Ford's is more adaptable than Dijkstra's algorithm, the latter is faster. While Dijkstra's method uses the concept of area relaxation but does not employ greedy techniques, Bellman-algorithm Ford's is dynamic and uses greedy approaches.

The benefits of this algorithm are:

1. Algorithm that is dynamic

2. Can calculate negative directed edges (in addition to positive ones), which can reduce network construction costs by determining the shortest path between two nodes so that fewer router paths are required.

3. The minimum path weight can be found using this algorithm with great accuracy and efficiency without the use of complicated data structures.

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