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Geodesic spanners for points on a polyhedral terrain

Abam, M. A ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1137/18M119358X
  3. Publisher: Society for Industrial and Applied Mathematics Publications , 2019
  4. Abstract:
  5. Let S be a set 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. © 2019 Society for Industrial and Applied Mathematics Publications. All rights reserved
  6. Keywords:
  7. Geometric spanners ; Polyhedral terrain ; Approximation algorithms ; Geodesy ; Geodesic distances ; Geometric spanner ; Lower bounds ; Polyhedral terrains ; Landforms
  8. Source: SIAM Journal on Computing ; Volume 48, Issue 6 , 2019 , Pages 1796-1810 ; 00975397 (ISSN)
  9. URL: https://epubs.siam.org/doi/abs/10.1137/18M119358X?mobileUi=0&