Understanding Dijkstra’s Algorithm

Dijkstra’s algorithm is an algorithm for finding the shortest paths between nodes in a weighted graph. This algorithm, which was conceived by computer scientist Edsger W. Dijkstra in 1956, was originally designed to find the shortest path between two given nodes. However, it is more commonly used to find the shortest paths from a single “source” node to all other nodes in the graph, producing a shortest-path tree.

How Dijkstra’s Algorithm Works

Dijkstra’s algorithm uses a greedy approach to calculate the shortest path from the source node to all other nodes in the graph. The algorithm maintains two sets of vertices:

• A set that contains vertices included in the shortest path tree (the shortest path tree set)
• Another set that includes vertices not yet included in the shortest path tree

At each step of the algorithm, it selects the vertex from the set of vertices not yet included that has the minimum distance from the source. Then, it calculates the distance through this vertex to each unvisited neighbor and updates the neighbor’s distance if it is smaller. This process continues until all vertices have been included in the shortest path tree.

Dijkstra’s algorithm uses labels that are positive integers or real numbers, which are totally ordered. It can be generalized to use any labels that are partially ordered, provided the subsequent labels have properties that ensure the algorithm’s correctness.

In the world of computer science and algorithms, there’s a lot of talk about Dijkstra’s algorithm and its classification as a “greedy” algorithm. In this article, we will explore what Dijkstra’s algorithm is, understand the concept of a greedy algorithm, and discuss whether or not Dijkstra’s algorithm qualifies as a greedy algorithm.