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

Jinhee Chun, Kunihiko Sadakane, Takeshi Tokuyama

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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 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 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 L 2-distance from the corresponding portion of f.

Original languageEnglish
Pages (from-to)103-115
Number of pages13
JournalAlgorithmica (New York)
Issue number2
Publication statusPublished - 2006 Feb
Externally publishedYes


  • Algorithms
  • Computational geometry
  • Curve simplification
  • Data analysis
  • Optimization

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics


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