The Floyd-Warshall algorithm is used to find the shortest paths between all pairs of vertices in a weighted graph. It works by iterating over each vertex and checking if going through another vertex results in a shorter path. One similarity with other algorithms like Dijkstra's and Bellman-Ford is that it also works with weighted graphs. One difference is that Floyd-Warshall can handle negative edge weights, while Dijkstra's and Bellman-Ford cannot.

Another algorithm that can be used for the same problem is the Johnson's algorithm, which first applies a transformation to the graph to eliminate negative edge weights before applying Dijkstra's algorithm. However, this additional step can be computationally expensive and may not be suitable for larger graphs.

In terms of performance, Floyd-Warshall has a time complexity of O(n^3), which can be quite slow for larger graphs. If the graph is sparse, a better performing algorithm is the Johnson's algorithm with Dijkstra's algorithm, which has a time complexity of O(mnlogn), where m is the number of edges and n is the number of vertices.

Overall, if you need to find the shortest paths between all pairs of vertices in a graph with negative edge weights, the Floyd-Warshall algorithm is the best option. However, if the graph is sparse, Johnson's algorithm with Dijkstra's algorithm may be a better choice for performance.
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