Coverage Problems in Wireless Adhoc Sensor Networks

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Coverage Problems in Wireless Ad-hoc Sensor
Networks

• Seapahn Meguerdichian1 Farinaz Koushanfar2
  Miodrag Potkonjak1 Mani Srivastava2

University of California, Los Angeles 1 Computer
Science Department 2 Electrical Engineering
Department
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Coverage Problem

• Given
• Field A
• N sensors, specified by coordinates
• Initial and final locations of an agent (I , F)
• How well can the field be observed ?
• Worst Case Coverage
• Find a maximal breach path for an agent moving
  in A.
• Best Case Coverage
• Find a maximal support path for an agent moving
  in A.

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Sensor Network Architecture
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Key Highlight

• Transform the difficult to represent coverage
  problems to discrete-domain optimization using
  computational geometry and graph theory
  constructs
• Voronoi Diagram
• Delaunay Triangulation

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Outline

• Sensing models and assumptions
• Coverage formulations
• Maximal Breach
• Maximal Support
• Interesting results
• Strengths and weaknesses
• Future directions
• Conclusion

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Sensing Model
We express the general sensing model S at an
arbitrary point p for a sensor s as
where d(s,p) is the Euclidean distance between
the sensor s and the point p, and positive
constants ? and K are sensor technology dependent
parameters
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Assumption

• Sensing effectiveness diminishes as distance
  increases (monotonic)
• Homogeneous sensor nodes
• Non-directional sensing technology
• Centralized computation model

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Coverage Formulation

• How well can the field be observed ?
• Worst Case Coverage Maximal Breach Path
• Best Case Coverage Maximal Support Path
• The paths are generally not unique. They
  quantify the best and worst case observability
  (coverage) in the sensor field.

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Maximal Breach

• Given Field A instrumented with sensors areas I
  and F.
• Problem Identify PB, the maximal breach path in
  S, starting in I and ending in F.
• PB is defined as a path with the property that
  for any point p on the path PB, the distance from
  p to the closest sensor is maximized.

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Enabling Step Voronoi Diagram
By construction, each line-segment maximizes
distance from the nearest point
(sensor). Consequence Path of Maximal Breach of
Surveillance in the sensor field lies on the
Voronoi diagram lines.
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Graph-Theoretic Formulation

• Given Voronoi diagram D with vertex set V and
  line segment set L and sensors S
• Construct graph G(N,E)
• Each vertex vi?V corresponds to a node ni ?N
• Each line segment li ?L corresponds to an edge ei
  ?E
• Each edge ei?E, Weight(ei) Distance of li from
  closest sensor sk ?S
• Formulation Is there a path from I to F which
  uses no edge of weight less than K?

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Finding Maximal Breach Path

• Algorithm
• Generate Voronoi Diagram
• Apply Graph-Theoretic Abstraction
• Search for PB
• Check existence of path I --gt F using BFS
• Search for path with maximal, minimum edge
  weights
• This is a Maximal Breach Path

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Bounded Voronoi Diagram
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Maximal Support

• Given Delaunay Triangulation
• of the sensor nodes
• Construct graph G(N,E)
• The graph is dual to the Voronoi graph previously
  described
• Formulation what is the path from which the
  agent can best be observed while moving from I to
  F? (The path is embedded in the Delaunay graph of
  the sensors)
• Solution Similar to the max breach algorithm,
  use BFS and Binary Search to find the shortest
  path on the Delaunay graph.

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Critical Regions
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Maximal Breach Path Example (50 nodes)
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Maximal Breach Path Example (200 nodes)
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Maximal Breach Sensor Deployment
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Maximal Support Sensor Deployment
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Asymptotic Behavior
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Localized Behavior
Using incremental techniques, we can handle
changes in node locations by locally adjusting
the diagram, rather than relying on global
re-calculations
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Future Directions

• Distributed Schemes
• Path planning
• Multi-sensor deployment optimization
• Average-case coverage calculations
• Exposure

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Conclusions

• Best and Worst case coverage formulations
• Efficient optimal algorithms using computational
  geometry and graph theory
• Maximal Breach Path (worst-case coverage)
• Maximal Support Path (best-case coverage)
• Applications in
• Deployment
• Asymptotic analysis