Linear time algorithm for approximating a curve by a single-peaked curve

Jinhee Chun, Kunihiko Sadakane, Takeshi Tokuyama

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsToshihide Ibaraki, Naoki Katoh, Hirotaka Ono
PublisherSpringer Verlag
Pages6-15
Number of pages10
ISBN (Electronic)9783540206958
DOIs
Publication statusPublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2906
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Chun, J., Sadakane, K., & Tokuyama, T. (2003). Linear time algorithm for approximating a curve by a single-peaked curve. In T. Ibaraki, N. Katoh, & H. Ono (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 6-15). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2906). Springer Verlag. https://doi.org/10.1007/978-3-540-24587-2_3