Dijkstra Algorithm Questions Long
In the Dijkstra Algorithm, edge weight updates refer to the process of modifying the weights assigned to the edges in a graph. These updates are crucial in determining the shortest path from a source vertex to all other vertices in the graph.
Initially, when the algorithm starts, all vertices except the source vertex are assigned a tentative distance value of infinity. The source vertex is assigned a distance value of 0. As the algorithm progresses, it explores the neighboring vertices of the current vertex and updates their tentative distance values if a shorter path is found.
Edge weight updates occur when the algorithm discovers a shorter path to a vertex that has already been visited. This happens when the current vertex's tentative distance value, combined with the weight of the edge connecting it to the neighboring vertex, is smaller than the neighboring vertex's current tentative distance value.
When an edge weight update occurs, the tentative distance value of the neighboring vertex is updated to the new, shorter distance. Additionally, the algorithm keeps track of the previous vertex that leads to this shorter path, allowing the algorithm to reconstruct the shortest path later.
The process of edge weight updates continues until all vertices have been visited or until the algorithm has found the shortest path to the target vertex. By iteratively updating the tentative distance values based on the weights of the edges, the Dijkstra Algorithm guarantees that the final distance values assigned to each vertex represent the shortest path from the source vertex.
It is important to note that the Dijkstra Algorithm assumes non-negative edge weights. If negative edge weights are present in the graph, the algorithm may produce incorrect results. In such cases, alternative algorithms like the Bellman-Ford Algorithm or the A* Algorithm can be used.