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Deployed as a natural environment observatory or a surveillance device, a remote networked robotic pan-tilt-zoom camera needs to be controlled by simultaneous frame requests from both online users and in situ sensors such as motion detectors. This paper presents algorithms that are capable of finding a camera frame that optimizes a measure of total satisfaction over all requests, which is a generalized version of the single frame-selection problem proposed by Song et al. in 2006.We present a lattice-based approximation algorithm; given n requests and approximation bound ∈, we analyze the tradeoff between solution quality and the corresponding computation time, and prove that the algorithm runs in O(n/∈3) time. We also develop a branch-and-bound-like implementation that reduces the constant factor of the algorithm by more than 70%. We have implemented the algorithms, and numerical experiment results conform to our analysis. Field experiments of the proposed algorithms have been conducted in the past three years. The proposed algorithms have been deployed successfully in a variety of real world applications including natural environment observation, building construction monitoring, and the surveillance of public space.