Fully Dynamic Sequential and Distributed Algorithms for MAX-CUT

This paper initiates the study of the MAX-CUT problem in fully dynamic graphs. Given a graph G = (V,E), we present deterministic fully dynamic distributed and sequential algorithms to maintain a cut on G which always contains at least |E|/2 edges in sublinear update time under edge insertions and deletions to G. Our results include the following deterministic algorithms: i) an O(Δ) worst-case update time sequential algorithm, where Δ denotes the maximum degree of G, ii) the first fully dynamic distributed algorithm taking O(1) rounds and O(Δ) total bits of communication per update in the Massively Parallel Computation (MPC) model with n machines and O(n) words of memory per machine. The aforementioned algorithms require at most one adjustment, that is, a move of one vertex from one side of the cut to the other.We also give the following fully dynamic sequential algorithms: i) a deterministic O(m^{1/2}) amortized update time algorithm where m denotes the maximum number of edges in G during any sequence of updates and, ii) a randomized algorithm which takes Õ(n^{2/3}) worst-case update time when edge updates come from an oblivious adversary.