### 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 |

Volume | 3827 LNCS |

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) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings*(Vol. 3827 LNCS, 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

**Sparse geometric graphs with small dilation.** / Aronov, Boris; De Berg, Mark; Cheong, Otfried; Gudmundsson, Joachim; Haverkort, Herman; Vigneron, Antoine.

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

*Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings.*vol. 3827 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3827 LNCS, pp. 50-59, 16th International Symposium on Algorithms and Computation, ISAAC 2005, Hainan, China, 12/19/05. https://doi.org/10.1007/11602613_7

}

TY - GEN

T1 - Sparse geometric graphs with small dilation

AU - Aronov, Boris

AU - De Berg, Mark

AU - Cheong, Otfried

AU - Gudmundsson, Joachim

AU - Haverkort, Herman

AU - Vigneron, Antoine

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33744953548&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33744953548&partnerID=8YFLogxK

U2 - 10.1007/11602613_7

DO - 10.1007/11602613_7

M3 - Conference contribution

SN - 3540309357

SN - 9783540309352

VL - 3827 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 50

EP - 59

BT - Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings

ER -