Network slicing enables diversified services to be carried in isolated slices. To maintain the quality of service and achieve high profit of a slice in dynamic environments, it is vital to agilely reconfigure the resource allocation for the slice. However, frequent reconfigurations also incur certain cost and might cause service interruption. To maximize the slice's profit and reduce the reconfiguration overhead, we propose a fast slice reconfiguration (FSR) scheme to cope with small traffic variations of individual slices at the time scale of flow arrival-departure. Due to small traffic variations, the FSR only reconfigures bandwidth and VNF capacity allocation for partial flows. We formulate the optimization problem for FSR, which is difficult to solve due to the discontinuity and non-convexity of the reconfiguration cost function. We propose to approximate the reconfiguration cost function with L1 norm, which preserves the sparsity of solution, thus avoiding unnecessary reconfigurations. Besides, the FSR problem should be solved efficiently, so that slices could be reconfigured timely. Hence, we exploit the dual-ADMM method to solve the problem in a distributed manner for large slices. Numerical results validate the effectiveness of the proposed FSR scheme and the distributed computing method for FSR problem.