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Progressive and approximate techniques are proposed here for ray-tracing systems used to predict radio propagation. In a progressive prediction system, intermediate prediction results are fed back to users continuously. As more raypaths are processed, the accuracy of prediction results improves progressively. We consider how to construct a progressive system that satisfies the requirements of continuous observability and controllability as well as faithfulness and fairness. Adding a workload estimator to such a progressive prediction system allows termination of the computation when a desired accuracy (mean and standard deviation of the error) is achieved without knowing the final result that would be obtained if the prediction system runs to completion. The sample generator is at the core of the progressive prediction system and serves to cluster and prioritize raypaths according to their expected contributions to prediction results. Two types of progressive approaches, source-group-raypath-permute and raypath-interleave, are proposed. The workload estimator determines the number of raypaths to be processed to achieve the specified requirement on prediction accuracy. Two approximate models are described that adjust the workload dynamically during the prediction process. Our experiments show that the proposed progressive and approximate methods provide flexible mechanisms to trade prediction accuracy for prediction time in a relatively fine granularity.