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Local Routing in Geometric Networks

Shahriari, Amir Hossein | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49630 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Abam, Mohammad Ali
  7. Abstract:
  8. A geometric network is a weighted undirected graph whose vertices are points in the plane and edge weights are equal to the Euclidean distance of its endpoints. Routing is one of the important problems in graph theory and if the underlying graph is a geometric network,it has applications in different fields including transportation, communication networks and robotics. In many applications the graph data is not accessible or finding the optimal path is costly. Therefore local routing is used. In local routing the goal is that at each vertex,the routing must be done only given the neighbours of the current vertex, the origin and the destination of the route. Geometric spanner is a subgraph of the complete graph where the shortest path between each pair of vertices is at most t times their shortest path in the original graph. In this study, local routing in geometric networks and specifically, geometric spanners will be examined. We show that deterministic local routing is not possible in a simple polygon. Then we present a local routing algorithm for well-separated pairs decomposition,which is a geometric spanner with many applications. About the impact of faults on local routing, we show that continuous Yao graph are tolerable against half-plane faults and we describe a local routing algorithm for it. Finally, we show that there is no deterministic local routing algorithm which is tolerable against all convex region faults
  9. Keywords:
  10. Geometric Spanner ; Fault Tolerance ; Routing Algorithm ; Geometric Networks ; Local Routing

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