Deterministic Min-cut in Poly-logarithmic Max-flows

We give a deterministic (global) min-cut algorithm for weighted undirected graphs that runs in time O(m
^1+ε
) plus polylog ( n) max-flow computations. Using the current best max-flow algorithms, this results in an overall running time of ~O(m·min(√m, n
^2/3
)) for weighted graphs, and m
^4/3+o(1)
for unweighted (multi)-graphs. This is the first improvement in the running time of deterministic algorithms for the min-cut problem on general (weighted/multi) graphs since the early 1990s when a running time bound of ~O(mn) was established for this problem.