### 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 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 single-peaked pieces under the condition that each single-peaked piece is within a fixed L_{2} distance from the corresponding portion of f.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Toshihide Ibaraki, Naoki Katoh, Hirotaka Ono |

Publisher | Springer Verlag |

Pages | 6-15 |

Number of pages | 10 |

ISBN (Electronic) | 9783540206958 |

DOIs | |

Publication status | Published - 2003 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2906 |

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