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Local geometric spanners

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

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  1. Type of Document: Article
  2. DOI: 10.1007/s00453-021-00860-5
  3. Publisher: Springer , 2021
  4. Abstract:
  5. We introduce the concept of local spanners for planar point sets with respect to a family of regions, and prove the existence of local spanners of small size for some families. For a geometric graph G on a point set P and a region R belonging to a family R, we define G∩ R to be the part of the graph G that is inside R (or is induced by R). A local t-spanner w.r.t R is a geometric graph G on P such that for any region R∈ R, the graph G∩ R is a t-spanner for K(P) ∩ R, where K(P) is the complete geometric graph on P. For any set P of n points and any constant ε> 0 , we prove that P admits local (1 + ε) -spanners of sizes O(nlog 6n) and O(nlog n) w.r.t axis-parallel squares and vertical slabs, respectively. If adding Steiner points is allowed, then local (1 + ε) -spanners with O(n) edges and O(nlog 2n) edges can be obtained for axis-parallel squares and disks using O(n) Steiner points, respectively. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature
  6. Keywords:
  7. Geometry ; Geometric graphs ; Geometric spanner ; Graph G ; Planar point sets ; Point set ; Steiner points ; Graph theory
  8. Source: Algorithmica ; Volume 83, Issue 12 , 2021 , Pages 3629-3648 ; 01784617 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s00453-021-00860-5