A Seemingly Polynomial-Time Algorithm for Optimal Curve Fitting by Segmented Straight Lines

Abstract

We consider least squares approximation of a function of one variable by a continuous, piecewise-linear approximand that has a small number of breakpoints. This problem was notably considered by Bellman who proposed an approximate algorithm based on dynamic programming. Many suboptimal approaches have been suggested, but so far, the only exact methods resort to mixed integer programming with superpolynomial complexity growth.In this paper, we present an exact and efficient algorithm based on dynamic programming with a hybrid value function. The achieved timecomplexity seems to be polynomial. * The authors are with the