Linear time algorithm for approximating a curve by a single-peaked curve
Given a function y = f(x) in one variable, we consider the problem of computing the single-peaked (unimodal) curve y =phi(x) minimizing the L-2-distance between them. If the input function f is a histogram with O(n) steps or a piecewise linear function with O(n) linear pieces, we design algorithms for computing phi in linear time. We also give an algorithm to approximate f with a function consisting of the minimum number of unimodal pieces under the condition that each unimodal piece is within a fixed L-2-distance from the corresponding portion of f.
algorithms computational geometry optimization data analysis curve simplification