Dijkstra Algorithm Questions
In the Dijkstra Algorithm, negative edge weights have a significant impact on the algorithm's functionality. The algorithm assumes that all edge weights are non-negative, and this assumption is crucial for its correctness and efficiency.
When negative edge weights are present, the Dijkstra Algorithm may not produce the correct shortest path or may fail to terminate. This is because the algorithm relies on the greedy approach of always selecting the vertex with the minimum distance from the source. However, negative edge weights can create cycles that continuously decrease the distance to a vertex, leading to an infinite loop.
To handle negative edge weights, a different algorithm called the Bellman-Ford Algorithm is typically used. The Bellman-Ford Algorithm can handle negative edge weights and detect negative cycles, but it has a higher time complexity compared to Dijkstra's Algorithm.