### Abstract

We show that, for any fixed δ > 0, the combinatorial complexity of the union of a triangles in the plane, each of whose angles is at least δ, is O(n2
^{α(n)} log* n). with the constant of proportionality depending oil δ. This considerably improves the twenty-year-old bound O(n log log n), due to Matoušek et al. [24, 25].

Original language | English (US) |
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Title of host publication | Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011 |

Pages | 1778-1785 |

Number of pages | 8 |

State | Published - 2011 |

Event | 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011 - San Francisco, CA, United States Duration: Jan 23 2011 → Jan 25 2011 |

### Other

Other | 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011 |
---|---|

Country | United States |

City | San Francisco, CA |

Period | 1/23/11 → 1/25/11 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011*(pp. 1778-1785)

**Improved bound for the union of fat triangles.** / Ezra, Esther; Aronov, Boris; Sharir, Micha.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011.*pp. 1778-1785, 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, San Francisco, CA, United States, 1/23/11.

}

TY - GEN

T1 - Improved bound for the union of fat triangles

AU - Ezra, Esther

AU - Aronov, Boris

AU - Sharir, Micha

PY - 2011

Y1 - 2011

N2 - We show that, for any fixed δ > 0, the combinatorial complexity of the union of a triangles in the plane, each of whose angles is at least δ, is O(n2 α(n) log* n). with the constant of proportionality depending oil δ. This considerably improves the twenty-year-old bound O(n log log n), due to Matoušek et al. [24, 25].

AB - We show that, for any fixed δ > 0, the combinatorial complexity of the union of a triangles in the plane, each of whose angles is at least δ, is O(n2 α(n) log* n). with the constant of proportionality depending oil δ. This considerably improves the twenty-year-old bound O(n log log n), due to Matoušek et al. [24, 25].

UR - http://www.scopus.com/inward/record.url?scp=79955744683&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955744683&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9780898719932

SP - 1778

EP - 1785

BT - Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011

ER -