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Geometric spanners for points inside a polygonal domain

Abam, M. A ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. DOI: 10.4230/LIPIcs.SOCG.2015.186
  3. Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 2015
  4. Abstract:
  5. Let P be a set of n points inside a polygonal domain D. A polygonal domain with h holes (or obstacles) consists of h disjoint polygonal obstacles surrounded by a simple polygon which itself acts as an obstacle. We first study t-spanners for the set P with respect to the geodesic distance function π where for any two points p and q, (p, q) is equal to the Euclidean length of the shortest path from p to q that avoids the obstacles interiors. For a case where the polygonal domain is a simple polygon (i.e., h = 0), we construct a (10 + ε)-spanner that has O(n log2 n) edges. For a case where there are h holes, our construction gives a (5 + ε)-spanner with the size of O(nh log2 n). Moreover, we study t-spanners for the visibility graph of P (V G(P), for short) with respect to a hole-free polygonal domain D. The graph V G(P) is not necessarily a complete graph or even connected. In this case, we propose an algorithm that constructs a (3 + ε)-spanner of size O(n4/3+δ). In addition, we show that there is a set P of n points such that any (3 - ε)-spanner of V G(P) must contain ω (n2) edges
  6. Keywords:
  7. Geometric Spanners ; Polygonal Domain ; Visibility Graph ; Computational geometry ; Graph theory ; Visibility ; Complete graphs ; Geodesic distances ; Geometric spanner ; Polygonal domain ; Shortest path ; Simple polygon ; Two-point ; Visibility graphs ; Geometry
  8. Source: 31st International Symposium on Computational Geometry, SoCG 2015, 22 June 2015 through 25 June 2015 ; Volume 34 , 2015 , Pages 186-197 ; 18688969 (ISSN) ; 9783939897835 (ISBN)
  9. URL: http://drops.dagstuhl.de/opus/volltexte/2015/5137