In this paper, we develop a new service to support optimally ensured user interactions with minimum latency in interactive distributed multimedia presentation environments. The novelty of our scheme is to reduce bandwidth requirements of a network in exchange of memory at the client side, because we expect an increase in network load in the next years in comparison to falling memory prices. Utilizing the properties of smoothing algorithms presented in the literature, we introduce the concepts of the interactive river bed and optimal interactive river bed, which guarantee optimal interactive service over the whole playback time of the video stream. Our approach provides optimal service for a given buffer size. We also derive requirements for a minimal buffer size in which we can give the optimal boundaries for an interactive transmission plan. Experiments demonstrate the effectiveness of the approach.