Dijkstra Algorithm Questions Long
In the Dijkstra Algorithm, vertex labeling is a crucial concept that helps in finding the shortest path from a source vertex to all other vertices in a weighted graph. It involves assigning labels or values to each vertex in the graph based on their current distance from the source vertex.
Initially, all vertices except the source vertex are labeled with an infinite value, indicating that their distance from the source is unknown. The source vertex is labeled with a value of 0, as it is the starting point of the algorithm.
As the algorithm progresses, it explores the neighboring vertices of the current vertex and updates their labels if a shorter path is found. The label of a vertex represents the minimum distance known so far from the source vertex to that particular vertex.
The algorithm selects the vertex with the minimum label among the unvisited vertices and considers it as the current vertex. It then examines all its neighboring vertices and calculates the distance from the source vertex through the current vertex. If this distance is smaller than the current label of the neighboring vertex, the label is updated with the new distance.
This process continues until all vertices have been visited or until the algorithm reaches the target vertex, if specified. The labels of the vertices are continuously updated as the algorithm progresses, ensuring that the shortest path is always considered.
Vertex labeling is essential in the Dijkstra Algorithm as it allows the algorithm to keep track of the shortest distance found so far for each vertex. By updating the labels, the algorithm gradually discovers the shortest path from the source vertex to all other vertices in the graph.
Overall, vertex labeling is a fundamental concept in the Dijkstra Algorithm that enables the algorithm to efficiently find the shortest path by assigning and updating labels representing the minimum distance from the source vertex to each vertex in the graph.