Efficient Piecewise-Linear Function Approximation Using the Uniform Metric

We give an O(n log n)-time method for nding a best k-link piecewise-linear function approximating an n-point planar data set using the well-known uniform metric to measure the error, 0, of the approximation. Our method is based upon new characterizations of such functions, which we exploit to design an eecient algorithm using a plane sweep in \ space" followed by several applications of the parametric searching technique. The previous best running time for this problem was O(n 2).