The paper "Computational Optimal Transport" by Gabriel Peyré and Marco Cuturi provides a comprehensive overview of optimal transport (OT) theory and its computational aspects. The authors begin by introducing the fundamental concepts of OT, such as histograms, measures, and the assignment and Monge problems. They then delve into the theoretical foundations, including the Kantorovich relaxation, metric properties of optimal transport, and the dual problem. The paper also covers algorithmic foundations, discussing linear programs, C-transforms, complementary slackness, and the network simplex method. Additionally, it explores entropic regularization, Sinkhorn's algorithm, and its convergence. The authors further examine the W1 optimal transport, both in metric spaces and Euclidean spaces, and its applications in imaging sciences and machine learning. The paper also discusses dynamic formulations, statistical divergences, and variational Wasserstein problems. Finally, it addresses extensions of OT, such as multimarginal problems, unbalanced optimal transport, and sliced Wasserstein distances. The authors emphasize the practical relevance of OT in data sciences and provide a detailed guide to efficient computational methods.The paper "Computational Optimal Transport" by Gabriel Peyré and Marco Cuturi provides a comprehensive overview of optimal transport (OT) theory and its computational aspects. The authors begin by introducing the fundamental concepts of OT, such as histograms, measures, and the assignment and Monge problems. They then delve into the theoretical foundations, including the Kantorovich relaxation, metric properties of optimal transport, and the dual problem. The paper also covers algorithmic foundations, discussing linear programs, C-transforms, complementary slackness, and the network simplex method. Additionally, it explores entropic regularization, Sinkhorn's algorithm, and its convergence. The authors further examine the W1 optimal transport, both in metric spaces and Euclidean spaces, and its applications in imaging sciences and machine learning. The paper also discusses dynamic formulations, statistical divergences, and variational Wasserstein problems. Finally, it addresses extensions of OT, such as multimarginal problems, unbalanced optimal transport, and sliced Wasserstein distances. The authors emphasize the practical relevance of OT in data sciences and provide a detailed guide to efficient computational methods.