Deterministic Min-cut in Poly-logarithmic Max-flows

Jason Li, Debmalya Panigrahi

Abstract: We give a deterministic (global) min-cut algorithm for weighted undirected graphs that runs in time O(m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1+ε</sup> ) 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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2/3</sup> )) for weighted graphs, and m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4/3+o(1)</sup> 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.