We address the problem of designing an efficient algorithm for computing the all-pairs shortest-time paths in time-varying networks, specifically targeting the dynamic topological characteristics of low earth orbit (LEO) satellite constellations. We model such temporal graphs as $G = (V, E_t)$, where $V=\{1, 2,\ldots , n\}$ is the set of $n$ vertices in the graph, and $E_t$ is the set of $M$ time-varying edges considered over a total time window of size $T = Mτ$, $τ$ being the duration of each interval in that time window. For such a network, our algorithm finds the all-pair shortest paths in $O(M^2n^3)$-time. A key advantage of our approach is its computational structure, which mirrors two matrix multiplication steps, first in the forward direction and then in the backward direction. This structure of the algorithm makes it exceptionally suitable for parallelization on SIMD architectures like GPUs, thereby offering a significant speedup over traditional shortest-path algorithms and enabling efficient, network-wide message routing in rapidly changing LEO satellite constellations.

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