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- Vigneron, Antoine
- Geometric Algorithms Lab.
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Sparse geometric graphs with small dilation
- Author(s)
- Aronov, Boris, Berg, Mark de, Cheong, Otfried, Gudmundsson, Joachim, Havekort, Herman, Vigneron, Antoine
- Issued Date
- 2005-12-19
- Citation
- 16th International Symposium on Algorithms and Computation, ISAAC 2005, pp.50 - 59
- 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.
- Publisher
- 16th International Symposium on Algorithms and Computation, ISAAC 2005
- ISSN
- 0302-9743
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