Before revision:  This breaks the natural barrier of O (\Delta) update time (where \Delta is the maximum degree in the graph) for vertex updates presented by Assadi et al. (STOC 2018).
After revision:  This breaks the natural barrier of \Omega (\Delta) update time (where \Delta is the maximum degree in the graph) for vertex updates presented by Assadi et al. (STOC 2018).