A collision-based Monte Carlo algorithm approximates multi-marginal optimal transport by random pairwise index swaps, running in O(n K^2 Np) time and O(n K Np) memory.
7, the proposed collision-based approach outperforms Sinkhorn in the distribution of relative error in the Wasserstein distance, speed-up and memory consumption
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Collision-based Dynamics for Multi-Marginal Optimal Transport
A collision-based Monte Carlo algorithm approximates multi-marginal optimal transport by random pairwise index swaps, running in O(n K^2 Np) time and O(n K Np) memory.