, Volume 44, Issue 2, pp 103–115

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


DOI: 10.1007/s00453-005-1201-y

Cite this article as:
Chun, J., Sadakane, K. & Tokuyama, T. Algorithmica (2006) 44: 103. doi:10.1007/s00453-005-1201-y


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 

Copyright information

© Springer 2005

Authors and Affiliations

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