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- Vigneron, Antoine
- Geometric Algorithms Lab.
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Sparse geometric graphs with small dilation
- Author(s)
- Aronov, Boris, de Berg, Mark, Cheong, Otfried, Gudmundsson, Joachim, Haverkort, Herman, Smid, Michiel, Vigneron, Antoine
- Issued Date
- 2008-08
- Citation
- COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, v.40, no.3, pp.207 - 219
- Abstract
- Given a set S of n points in R(D), 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, maximum degree five, and dilation O(n/(k + 1)) can be computed in time O(n log n). For any k, we also construct planar n-point sets for which any geometric graph with n - 1 + k edges has dilation Omega (n/(k + 1)); a slightly weaker statement holds if the points of S are required to be in convex position. (c) 2007 Elsevier B.V. All rights reserved
- Publisher
- ELSEVIER SCIENCE BV
- ISSN
- 0925-7721
- Keyword (Author)
- dilation, spanner, geometric network, small-dilation spanning tree
- Keyword
- MINIMUM SPANNING-TREES, POINT SETS, SPANNERS, NETWORKS
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