The Floyd-Warshall algorithm is used to find the shortest paths in a weighted graph that may have negative edge weights but no negative cycles. It considers all possible paths between any two vertices and updates the shortest path values accordingly. Although it has a time complexity of O(N^3), it is useful for finding shortest paths between all pairs of vertices. On the other hand, Johnson's algorithm is an improvement over the Floyd-Warshall algorithm and works with graphs that may have negative edge weights and negative cycles. It transforms the graph using a potential function and then runs Dijkstra's algorithm on the transformed graph. Johnson's algorithm has a time complexity of O(N^2 log N + N * M), where N is the number of vertices and M is the number of edges in the graph.

In summary, both the Floyd-Warshall and Johnson's algorithms are used to find shortest paths in weighted graphs. However, the Floyd-Warshall algorithm works only with graphs that have no negative cycles, while Johnson's algorithm works with graphs that may have negative cycles. Johnson's algorithm is more efficient than the Floyd-Warshall algorithm in such cases, but has a higher time complexity.
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