[PDF] dijkstra algorithm complexity analysis

What is the time complexity of Dijkstra's algorithm?

Dijkstra’s algorithm has a time complexity of O (V^2) for a dense graph and O (E log V) for a sparse graph, where V is the number of vertices and E is the number of edges in the graph. The time complexity of A* algorithm depends on the quality of the heuristic function. .

What is the difference between Dijkstra's algorithm and Bellman-Ford algorithm?

Dijkstra's algorithm is usually the working principle behind link-state routing protocols, OSPF and IS-IS being the most common ones. Unlike Dijkstra's algorithm, the Bellman–Ford algorithm can be used on graphs with negative edge weights, as long as the graph contains no negative cycle reachable from the source vertex s.

Is Dijkstra's heuristic function admissible?

This heuristic function is admissible, meaning that it never overestimates the actual distance to the goal node Dijkstra’s algorithm has a time complexity of O (V^2) for a dense graph and O (E log V) for a sparse graph, where V is the number of vertices and E is the number of edges in the graph.

How to calculate run time using binary heaps using Dijkstra's algorithm?

let n be the number of vertices and m be the number of edges. Since with Dijkstra's algorithm you have O (n) delete-min s and O (m) decrease_key s, each costing O (logn), the total run time using binary heaps will be O (log (n) (m + n)).