In this paper we focus on the problem of continuously monitoring the set of Reverse k-Nearest Neighbors (RkNNs) of a query object in a moving object database using a client server architecture. The RkNN monitoring query computes for a given query object q, the set RkNN(q) of objects having q as one of their k-nearest neighbors for each point in time. In our setting the central server can poll the exact positions of the clients if needed. However in contrast to most existing approaches for this problem we argue that in various applications, the limiting factor is not the computational time needed but the amount of traffic sent via the network. We propose an approach that minimizes the amount of communication between clients and central server by an intelligent approximation of the position of the clients. Additionally we propose several poll heuristics in order to further decrease the communication costs. In the experimental section we show the significant impact of our proposed impr...