Mathematical Methods for Optimization
The Bellman-Ford algorithm is a graph search algorithm used to find the shortest paths from a single source vertex to all other vertices in a weighted graph, accommodating graphs with negative weight edges. It works by repeatedly relaxing the edges and ensuring that the shortest path estimates are updated accordingly, even allowing detection of negative cycles. This algorithm is particularly important in the context of shortest path problems, as it can handle scenarios where other algorithms, like Dijkstra's, may fail due to negative weights.
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