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Asymptotically Optimal Mobile Ad-Hoc Routing

Asymptotically Optimal Mobile Ad-Hoc Routing. Fabian Kuhn Roger Wattenhofer Aaron Zollinger. Overview. Introduction Model Face Routing Adaptive Face Routing Lower Bound Conclusion. Model I (Ad-Hoc Network). Nodes are points in R 2

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Asymptotically Optimal Mobile Ad-Hoc Routing

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  1. Asymptotically Optimal Mobile Ad-Hoc Routing Fabian Kuhn Roger Wattenhofer Aaron Zollinger

  2. Overview • Introduction • Model • Face Routing • Adaptive Face Routing • Lower Bound • Conclusion Distributed Computing Group

  3. Model I (Ad-Hoc Network) • Nodes are points in R2 • All nodes have the same transmission range (normalized to 1)) network is a unit disk graph • Distance between any two nodes is lowerbounded by a constant d0)W(1)-model Distributed Computing Group

  4. Model II (Geometric Routing) • Nodes know the geometric positions of themselves and of their neighbors • Source s knows the coordinates of destination t • Nodes not allowed to store anything • In the message, only O(logn) additional bits can be stored Distributed Computing Group

  5. Cost Model I • Cost of sending a message over a link (edge) e is c(e) • Cost of a path p is the sum over the costs of its edges • Cost of a routing algorithm A is the sum over the costs of the traversed edges Distributed Computing Group

  6. Cost Model II 3 different cost metrics: • Link distance metric (c(e)´1) • Euclidean distance (cd(e)) • Energy metric (cE(e):=cd2(e))more general: cE(e):=cda(e) for an a¸2 Distributed Computing Group

  7. Costs are Equivalent Lemma: In the W(1)-model the link, Euclidean, and energy metrics of a path or an algorithm are equivalent up to a constant factor. Distributed Computing Group

  8. Face Routing geometric routing algorithm for planar graphs Compass Routing on Geometric Networks [Kranakis, Singh, Urrutia; 1999] Distributed Computing Group

  9. Face Routing Distributed Computing Group

  10. Face Routing (Faces) Distributed Computing Group

  11. Face Routing s t Distributed Computing Group

  12. Face Routing s t Distributed Computing Group

  13. Face Routing s t Distributed Computing Group

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  36. Face Routing s t Distributed Computing Group

  37. Face Routing (Analysis) Lemma: Face Routing always finds a path to the destination. The total cost of Face Routing is O(n). Distributed Computing Group

  38. ) each edge is traversed at most four times Face Routing (Analysis) Proof Sketch: • each face is explored at most once • there are at most 3n-6 edges (Euler formula) Distributed Computing Group

  39. Problem of Face Routing • Face Routing always reaches destination • However, even if source and destination are close to each other, Face Routing can take O(n) steps. • We would like to have an algorithm, whose cost is a function of the cost of an optimal path. Distributed Computing Group

  40. Adaptive Face Routing s t Distributed Computing Group

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  50. Adaptive Face Routing Ellipse is too small, go back! s t Distributed Computing Group

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