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Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for this problem using the l∞ norm, and we present an optimal linear time algorithm based on novel formalism. Moreover, given a precomputation in time O(n log n) consisting of a labeling of all extrema, we compute any optimal segmentation in constant time. Wedoi:10.1109/icdm.2005.25 dblp:conf/icdm/LemireBY05 fatcat:dclz46zkp5akjkvryoqdqc2rgm