Consider how matrix multiplication can be used to compute shortest paths, and recall that the Floyd-Warshall algorithm also solves APSP but with a time complexity of O(V³).

Explore the idea of using exponentiation by squaring on the adjacency matrix to reduce the time complexity, and think about how this can be combined with matrix multiplication.

Investigate the use of Strassen's algorithm for matrix multiplication, which has a time complexity of O(V^log₂7), and analyze how this can be applied to the APSP problem to achieve the desired time complexity.