In the CLRS book it says that "relabel to front" algorithm, which solves the maximum-flow problem, maintains a list of topologically sorted vertices in the admissible network and that vertices with zero excess flow are moved to the front of the list.
I do not fully understand what is the meaning of it.
I would imagine that the vertices are sorted according to the number of admissible edges incident on it. But then how would moving vertices with no excess flow to front affects the sorting order in this case. Also how come the list is already sorted when it is initialized with random order of vertices?
Just realized that topological sorting of vertices in the admissible network means that for every admissible edge (u,v) in the admissible network the vertex u appears before v in the list.
This does not answer the last two parts of my question though, how is that the list is already sorted when initialized and how does moving zero-excess-flow vertices to front affect the order. Thanks.