Algorithmica

, Volume 44, Issue 2, pp 103–115

Linear Time Algorithm for Approximating a Curve by a Single-Peaked Curve

Article

Abstract

Given a function y = f(x) in one variable, we consider the problem of computing the single-peaked (unimodal) curve y =φ(x) minimizing the L2-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 φ 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 L2-distance from the corresponding portion of f.

Computational geometry Optimization Data analysis Algorithms Curve simplification 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.GSIS, Tohoku University, SendaiJapan
  2. 2.Graduate School of System Information Science, Kyushu University, HakozakiJapan

Personalised recommendations