Shortest path, Dijkstra's algorithm

This lecture explains Dijkstra's algorithm for finding the shortest path in a network with non-negative costs, showing how each node is treated at most once and how the labels become permanent. The algorithm initializes labels and iterates through nodes, updating labels and selecting nodes based on the smallest label. The lecture demonstrates the properties of the algorithm, proving that once a label is set, it remains unchanged, leading to the selection of the shortest path. Dijkstra's algorithm simplifies the generic shortest path algorithm by assuming non-negative costs and introducing a rule for node selection, ensuring efficiency and accuracy in finding the shortest path.