@inbook{a649859f23eb4630b2bd99e287c86bcc,
title = "Linear time algorithm for approximating a curve by a single-peaked curve",
abstract = "Given a function y = f(x) in one variable, we consider the problem of computing the single-peaked 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 single-peaked pieces under the condition that each single-peaked piece is within a fixed L2 distance from the corresponding portion of f.",
author = "Jinhee Chun and Kunihiko Sadakane and Takeshi Tokuyama",
year = "2003",
doi = "10.1007/978-3-540-24587-2_3",
language = "English",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "6--15",
editor = "Toshihide Ibaraki and Naoki Katoh and Hirotaka Ono",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
address = "Germany",
}