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In this paper, we present an adaptive search algorithm to automatically select the scaling range in the wavelet-based Hurst parameter estimation method. This algorithm is recursive and adaptive in nature, and it can select a scaling range consistent with human visual selection. In addition, it can be easily extended to automatically find the (approximately) linear regions of any curve. We tested our algorithm on 13 NLANR network traffic traces. The results show that our algorithm works well for the cases of monofractal traffic.