Here are some general strategies that can be applied to improve the time complexity of the Floyd-Warshall algorithm:

Parallelization: The Floyd-Warshall algorithm can be parallelized to run on multiple processors or computers. This can significantly reduce the time complexity for larger graphs.

Memoization: Memoization can be used to store the intermediate results of the Floyd-Warshall algorithm. This can avoid redundant calculations and reduce the time complexity.

Sparse matrix representation: The Floyd-Warshall algorithm uses a matrix to store the shortest paths between all pairs of vertices. However, if the graph is sparse, i.e., it has few edges compared to the total number of possible edges, a sparse matrix representation can be used to reduce the memory usage and improve the time complexity.

Early termination: If the Floyd-Warshall algorithm finds that no improvement is possible for a particular vertex, it can terminate early and move on to the next vertex. This can reduce the number of iterations and improve the time complexity.

Heuristics: Some heuristics can be applied to the Floyd-Warshall algorithm to reduce the number of iterations or to avoid unnecessary calculations. For example, if the graph has a large number of negative edges, the algorithm can first check if any negative cycle exists before proceeding with the iterations.

These are just a few strategies that can be applied to optimize the Floyd-Warshall algorithm. However, the actual optimizations will depend on the specific characteristics of the graph and the available resources.
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