Motivation

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Hybrid-Z Geographic Routing Without Location
Information using Dual Realities in Virtual Space
Manish Shah, Jaspal S. Sandhu manish007_at_berkele
y.edu, jaspal_at_me.berkeley.edu Computer Science
Division Department of Mechanical
Engineering University of California,
Berkeley ACKNOWLEDGEMENTS David Ratajczak,
Ananth Rao, Christos Papadimitriou, Ion Stoica
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Motivation

• Large wireless communication systems require
  scalable routing ? geographic routing
• Location information not always available (e.g.
  sensor networks), but this information not always
  necessary for geographic routing Rao et al 03
• Even without location information, expensive
  methods needed for dead-ends, voids (e.g.
  expanding ring, GPSR)

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Concept

• Construct convex polyhedron from planar graph
  Grünbaum 75 of virtual x-y coordinates
• Greedy method reduce angle between
  (currentNode,origin) (origin,dstNode)

polyhedral generation using Hybrid-Z
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Network Initialization

• Perimeter node self-discovery using common
  heuristic
• Perimeter node mapping to virtual circle
• Weighted rubberbanding accelerates convergence

weighted rubber-banding results for (left to
right) 1, 5 10 iterations
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Hybrid-Z Greedy Routing Protocol

• Destination coordinates (x,y,z) are known
• Attempt to make progress minimizing 2D Euclidean
  distance (x-y)
• If no further progress can be made, switch to 3D
  greedy routing based on convex polyhedron
• Minimize angle between vectors connecting
• polyhedral origin to next hop
• polyhedral origin to destination

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Assumptions Simulation

• Assumptions
• Perfect radio range
• No packet loss
• Simulator
• constructs random meshes
• initializes virtual coordinates
• generates path between random (src,dst) pairs

routing in virtual space using Hybrid-Z (top view)
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Results Evaluation

• 10 network generations, 1000 random pairs per
  trial, comparing Hybrid-Z to 2D greedy routing
• 3200 nodes, radio range 8
• high (200x200) and low (250x250) density

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Other Scenarios

• Attempt 3D greedy routing
• If no further progress possible, two
  alternatives
• BEST-Z
• route to neighbor with highest z coordinate
• shown to be more successful than pure 3D routing,
  but still not as effective as pure 2D
• ZtoXY
• route using greedy 2D Euclidean distance
• better than pure 2D and pure 3D routing
• Hybrid-Z outperforms ZtoXY in routing success

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Conclusions Future Work

• Extension to Rao et al 03 allows for more
  effective greedy routing without the need for
  non-greedy, communication-intensive mechanisms
  such as expanding ring
• Hybrid-Z method simplifies protocol and minimizes
  energy expenditures due to radio communication
• Future work
• Better methods for virtual coordinate
  initialization
• Consider mobility issues