### Abstract

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 language | English |
---|---|

Pages (from-to) | 103-115 |

Number of pages | 13 |

Journal | Algorithmica (New York) |

Volume | 44 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 Feb 1 |

### Keywords

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

### ASJC Scopus subject areas

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

## Fingerprint Dive into the research topics of 'Linear time algorithm for approximating a curve by a single-peaked curve'. Together they form a unique fingerprint.

## Cite this

Chun, J., Sadakane, K., & Tokuyama, T. (2006). Linear time algorithm for approximating a curve by a single-peaked curve.

*Algorithmica (New York)*,*44*(2), 103-115. https://doi.org/10.1007/s00453-005-1201-y