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Geometric Spanners in Polygonal Domains

Adeli, Marjan | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45530 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Abam, Mohammad Ali
  7. Abstract:
  8. A geometric network is an undirected weighted graph whose vertices are defined as points in a geometric space, such as the real d-dimensional space. The weight of each edge of the network is equal to the Euclidean distance between the two endpoints of that edge.Geometric networks are used to model many real systems such as roads, communication networks, etc. When designing a network, one may consider different criteria. For lots of applications, existence of a short path between any two points of the network is important. The direct connection between any two points of a network is the ideal lution; however, this not possible in many applications because of its high cost. In order to reduce the number of the edges and maintain the short paths between any two points, t-spanner networks are introduced.. A t-spanner network (t > 1), is a network in which the maximum distance between any two points is at most t times of the direct distance between those two points. Several t-spanner networks have been proposed so far. In this thesis, the problem of finding a t-spanner of the complete graph G in the metric space (S, π) is described; with S being the set of n points inside a simple polygon, and the function π on S being the geodesic distance (the shortest path) etween any two points of S inside the polygon P . The problem has been solved for the simple case of a polygon P with no obstacles inside and the complex case of a polygon P with several convex polygonal obstacles inside. For the former, we propose an algorithm that build a (4 + ϵ)-spanner with linear size O(n log2n) and diameter 2. Then, we extend the algorithm to the case of polygon P with h convex obstacles to make a (4 + ϵ)-spanner with size O(nh log2 n) and diameter 2
  9. Keywords:
  10. Geometric Spanner ; T-Spanner ; Geodesic Distance ; Semi-Seperated Pair Decomposition

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