Optimal assignment using the Hungarian algorithm was found to be improved for optimal transport using the Sinkhorn algorithm.
Intuitively I cannot make out why. More fundamentally, how optimal assignment is different from optimal transport, if it even is. If an explanation of the title question can be made based on the differences between the Hungarian objective function and the Sinkhorn objective function/protocol, this might help with understanding.
Also, does Sinkhorn algorithm = Sinkhorn-Knopp algorithm = Sinkhorn's theorem?