Efficient piecewise-linear function approximation using the uniform metric
TL;DR: An anO(n logn)-time method for finding a bestk-link piecewise-linear function approximating ann-point planar point set using the well-known uniform metric to measure the error, ε≥0, of the approximation.
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Abstract: We given anO(n logn)-time method for finding a bestk-link piecewise-linear function approximating ann-point planar point set using the well-known uniform metric to measure the error, ??0, of the approximation. Our methods is based upon new characterizations of such functions, which we exploit to design an efficient algorithm using a plane sweep in "? space" followed by several applications of the parametric-searching technique. The previous best running time for this problems wasO(n2).
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