Dijkstra Algorithm Questions Long
In the Dijkstra Algorithm, edge relaxation is a crucial step that helps determine the shortest path from a source vertex to all other vertices in a weighted graph. It involves continuously updating the distance values of vertices as the algorithm progresses.
During the execution of the algorithm, each vertex is assigned a tentative distance value, which represents the current shortest distance from the source vertex to that particular vertex. Initially, the source vertex is assigned a distance value of 0, while all other vertices are assigned a distance value of infinity.
Edge relaxation is performed when exploring the neighboring vertices of a particular vertex. For each neighboring vertex, the algorithm checks if the distance from the source vertex to the current vertex, plus the weight of the edge connecting them, is less than the tentative distance value of the neighboring vertex. If it is, the tentative distance value of the neighboring vertex is updated to the new, shorter distance.
This process is repeated for all the neighboring vertices of the current vertex, ensuring that the shortest path to each neighboring vertex is considered. By continuously updating the tentative distance values, the algorithm gradually determines the shortest path from the source vertex to all other vertices in the graph.
The edge relaxation step is crucial in guaranteeing the correctness of the Dijkstra Algorithm. It ensures that the algorithm explores all possible paths and updates the distance values accordingly, ultimately leading to the determination of the shortest path. Without edge relaxation, the algorithm would not be able to accurately find the shortest path in a weighted graph.