@inproceedings{11806,
  abstract     = {This paper presents insertions-only algorithms for maintaining the exact and approximate size of the minimum edge cut and the minimum vertex cut of a graph. The algorithms output the approximate or exact size k in time O(1) or O(log n) and a cut of size k in time linear in its size. The amortized time per insertion is O(1/ε 2) for a (2+ε)-approximation, O((log λ)((log n)/ε)2) for a (1+ε)-approximation, and O(λ log n) for the exact size of the minimum edge cut, where n is the number of nodes in the graph, λ is the size of the minimum cut and ε>0. The (2+ε)-approximation algorithm and the exact algorithm are deterministic, the (1+ε)-approximation algorithm is randomized. The algorithms are optimal in the sense that the time needed for m insertions matches the time needed by the best static algorithm on a m-edge graph. We also present a static 2-approximation algorithm for the size κ of the minimum vertex cut in a graph, which takes time O(n 2 min(√n,κ)). This is a factor of κ faster than the best algorithm for computing the exact size, which takes time O(κ 2 n 2 +κ 3 n 1.5). We give an insertionsonly algorithm for maintaining a (2+ε)-approximation of the minimum vertex cut with amortized insertion time O(n(logκk)/ε).},
  author       = {Henzinger, Monika H},
  booktitle    = {22nd International Colloquium on Automata, Languages and Programming},
  isbn         = {9783540494256},
  issn         = {1611-3349},
  location     = {Szeged, Hungary},
  pages        = {280–291},
  publisher    = {Springer Nature},
  title        = {{Approximating minimum cuts under insertions}},
  doi          = {10.1007/3-540-60084-1_81},
  volume       = {944},
  year         = {1995},
}