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A cut tree (or Gomory-Hu tree) of an undirected weighted graph G=(V,E)encodes a minimum s-t-cut for each vertex pair {s,t} \subseteq V and can beiteratively constructed by n-1 maximum flow computations. They solve themultiterminal network flow problem, which asks for the all-pairs maximum flowvalues in a network and at the same time they represent n-1 non-crossing,linearly independent cuts that constitute a minimum cut basis of G. Hence, cuttrees are resident in at least two fundamental fields of network analysis andgraph theory, which emphasizes their importance for many applications. In thiswork we present a fully-dynamic algorithm that efficiently maintains a cut treefor a changing graph. The algorithm is easy to implement and has a highpotential for saving cut computations under the assumption that a local changein the underlying graph does rarely affect the global cut structure. Wedocument the good practicability of our approach in a brief experiment on realworld data.

Dynamic Gomory-Hu Tree Construction -- fast and simple