Williams (APSP on Dense Directed Graphs with Arbitrary Weights All-Pairs Shortest Paths (APSP))
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Time Complexity
$O(n^{3} /{2}^{(\log n)^{0.5}})$
Space Complexity
$O(n^{2})$ words
(Derived: discussed with Ryan, uses an auxiliary $V \times V$ matrix, and the space required for the matrix multiplication of $V \times d$ and $d \times V$ matrices is also $O(V^2)$)
Description
Approximate?
Exact
Randomized?
No, deterministic
Model of Computation
Word RAM
Year
2014