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Geodesic spanners for points on a polyhedral terrain

Abam, M. A ; Sharif University of Technology | 2017

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  1. Type of Document: Article
  2. DOI: 10.1137/1.9781611974782.161
  3. Publisher: Association for Computing Machinery , 2017
  4. Abstract:
  5. Let S be a set S of n points on a polyhedral terrain T in R3, and let ϵ > 0 be a fixed constant. We prove that S admits a (2 + ϵ)-spanner with O(n log n) edges with respect to the geodesic distance. This is the first spanner with constant spanning ratio and a near-linear number of edges for points on a terrain. On our way to this result, we prove that any set of n weighted points in Rd admits an additively weighted (2 + ϵ)-spanner with O(n) edges; this improves the previously best known bound on the spanning ratio (which was 5 + ϵ), and almost matches the lower bound. Copyright © by SIAM
  6. Keywords:
  7. Geodesy ; Geodesic distances ; Lower bounds ; Polyhedral terrains ; Landforms
  8. Source: 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, 16 January 2017 through 19 January 2017 ; 2017 , Pages 2434-2442 ; 9781611974782 (ISBN)
  9. URL: https://epubs.siam.org/doi/abs/10.1137/1.9781611974782.161