### Abstract

Given a set S of n points in the plane, and an integer k such that 0 ≤ k < n, we show that a geometric graph with vertex set S, at most n - 1 + k edges, and dilation O(n/(k + 1)) can be computed in time O(n log n). We also construct n-point sets for which any geometric graph with n - 1 + k edges has dilation Ω(n/(k + 1)); a slightly weaker statement holds if the points of S are required to be in convex position.

Original language | English (US) |
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Title of host publication | Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings |

Pages | 50-59 |

Number of pages | 10 |

DOIs | |

State | Published - 2005 |

Event | 16th International Symposium on Algorithms and Computation, ISAAC 2005 - Hainan, China Duration: Dec 19 2005 → Dec 21 2005 |

### 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 | 3827 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 16th International Symposium on Algorithms and Computation, ISAAC 2005 |
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Country | China |

City | Hainan |

Period | 12/19/05 → 12/21/05 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Aronov, B., De Berg, M., Cheong, O., Gudmundsson, J., Haverkort, H., & Vigneron, A. (2005). Sparse geometric graphs with small dilation. In

*Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings*(pp. 50-59). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3827 LNCS). https://doi.org/10.1007/11602613_7