### Abstract

A new upper bound is shown for the number of incidences between n points and n families of concentric circles in the plane. As a consequence, it is shown that the number of the k most frequent distances among n points in the plane is f_{n}(k) = O(n^{1.4571}k^{.6286}) improving on an earlier bound of Akutsu, Tamaki, and Tokuyama.

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

Pages (from-to) | 639-648 |

Number of pages | 10 |

Journal | Discrete & Computational Geometry |

Volume | 28 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2002 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology

### Cite this

*Discrete & Computational Geometry*,

*28*(4), 639-648. https://doi.org/10.1007/s00454-002-2896-z

**The k most frequent distances in the plane.** / Solymosi, József; Tardos, G.; Tóth, Csaba D.

Research output: Contribution to journal › Article

*Discrete & Computational Geometry*, vol. 28, no. 4, pp. 639-648. https://doi.org/10.1007/s00454-002-2896-z

}

TY - JOUR

T1 - The k most frequent distances in the plane

AU - Solymosi, József

AU - Tardos, G.

AU - Tóth, Csaba D.

PY - 2002

Y1 - 2002

N2 - A new upper bound is shown for the number of incidences between n points and n families of concentric circles in the plane. As a consequence, it is shown that the number of the k most frequent distances among n points in the plane is fn(k) = O(n1.4571k.6286) improving on an earlier bound of Akutsu, Tamaki, and Tokuyama.

AB - A new upper bound is shown for the number of incidences between n points and n families of concentric circles in the plane. As a consequence, it is shown that the number of the k most frequent distances among n points in the plane is fn(k) = O(n1.4571k.6286) improving on an earlier bound of Akutsu, Tamaki, and Tokuyama.

UR - http://www.scopus.com/inward/record.url?scp=0036883299&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036883299&partnerID=8YFLogxK

U2 - 10.1007/s00454-002-2896-z

DO - 10.1007/s00454-002-2896-z

M3 - Article

AN - SCOPUS:0036883299

VL - 28

SP - 639

EP - 648

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 4

ER -