Block Coordinate Descent Network Simplex Methods for Optimal Transport
Abstract
We propose the Block Coordinate Descent Network Simplex (BCDNS) method for solving large-scale discrete Optimal Transport (OT) problems. BCDNS integrates the Network Simplex (NS) algorithm with a block coordinate descent (BCD) strategy, decomposing the full problem into smaller subproblems per iteration and reusing basis variables to ensure feasibility. We prove that BCDNS terminates in a finite number of iterations with an exact optimal solution, and we characterize its per-iteration complexity as O(s N), where s is a user-defined parameter in (0,1) and N is the total number of variables. Numerical experiments demonstrate that BCDNS matches the classical NS method in solution accuracy, reduces memory footprint compared to the Sinkhorn algorithm, achieves speed-ups of up to tens of times over the classical NS method, and exhibits runtime comparable to a high-precision Sinkhorn implementation.
Cite
@article{arxiv.2506.21231,
title = {Block Coordinate Descent Network Simplex Methods for Optimal Transport},
author = {Lingrui Li and Nobuo Yamashita},
journal= {arXiv preprint arXiv:2506.21231},
year = {2026}
}