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Geodesic spanners for points in R3 amid axis-parallel boxes

Abam, M. A ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ipl.2020.106063
  3. Publisher: Elsevier B.V , 2021
  4. Abstract:
  5. Let P be a set of n points in R3 amid a bounded number of obstacles. Consider the metric space M=(P,dM) where dM(p,q) is the geodesic distance of p and q, i.e., the length of a shortest path from p to q avoiding obstacles. When obstacles are axis-parallel boxes, we prove that M admits an 83-spanner with O(nlog3⁡n) edges. In other words, let S be a complete graph on n vertices where each node corresponds to a point p∈P. For nodes u and v of S corresponding to p,q∈P, the edge (u,v) is associated with the geodesic distance of p and q as its weight. We indeed prove that S admits a near linear-size t-spanner for some constant t. © 2020 Elsevier B.V
  6. Keywords:
  7. Geodesy ; Graph structures ; Avoiding obstacle ; Complete graphs ; Geodesic distances ; Metric spaces ; Shortest path ; Graph theory
  8. Source: Information Processing Letters ; Volume 166 , 2021 ; 00200190 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0020019020301502