Tag Archives: Richard E. Bellman

Computer Algorithms: Bellman-Ford Shortest Path in a Graph

Introduction

As we saw in the previous post, the algorithm of Dijkstra is very useful when it comes to find all the shortest paths in a weighted graph. However it has one major problem! Obviously it doesn’t work correctly when dealing with negative lengths of the edges.

We know that the algorithm works perfectly when it comes to positive edges, and that is absolutely normal because we try to optimize the inequality of the triangle.

Dijkstra's Approach
Since all the edges are positive we get the closest one!

Since Dijkstra’s algorithm make use of a priority queue normally we get first the shortest adjacent edge to the starting point. In our very basic example we’ll get first the edge with the length of 3 -> (S, A).

However when it comes to negative edges we can’t use any more priority queues, so we need a different, yet working solution. Continue reading Computer Algorithms: Bellman-Ford Shortest Path in a Graph