Solving a Special Type of Optimal Transport Problem by a Modified Hungarian Algorithm
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We observe that computing empirical Wasserstein distance in the independence test is an optimal transport (OT) problem with a special structure. This observation inspires us to study a special type of OT problem and propose a modified Hungarian algorithm to solve it exactly. For an OT problem between marginals with m and n atoms (m≥ n), the computational complexity of the proposed algorithm is O(m^2n). Computing the empirical Wasserstein distance in the independence test requires solving this special type of OT problem, where we have m=n^2. The associate computational complexity of our algorithm is O(n^5), while the order of applying the classic Hungarian algorithm is O(n^6). Numerical experiments validate our theoretical analysis. Broader applications of the proposed algorithm are discussed at the end.
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