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Interactive data visualization and exploration (DVE) applications are often network-bottlenecked due to bursty request patterns, large response sizes, and heterogeneous deployments over a range of networks and devices. This makes it difficult to ensure consistently low response times (< 100ms). Khameleon is a framework for DVE applications that uses a novel combination of prefetching and response tuning to dynamically trade-off response quality for low latency. Khameleon exploits DVE's approximation tolerance: immediate lower-quality responses are preferable to waiting for complete results. To this end, Khameleon progressively encodes responses, and runs a server-side scheduler that proactively streams portions of responses using available bandwidth to maximize user's perceived interactivity. The scheduler involves a complex optimization based on available resources, predicted user interactions, and response quality levels; yet, decisions must also be real-time. To overcome this, Khameleon uses a fast greedy approximation which closely mimics the optimal approach. Using image exploration and visualization applications with real user interaction traces, we show that across a wide range of network and client resource conditions, Khameleon outperforms classic prefetching approaches that benefit from perfect prediction models: response latencies with Khameleon are never higher, and typically between 2 to 3 orders of magnitude lower while response quality remains within 50%-80%.