Exposure In Wireless AdHoc Sensor Networks

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Exposure In Wireless Ad-Hoc Sensor Networks
Seapahn Meguerdichian Computer Science
Department University of California, Los Angeles
Farinaz Koushanfar Department of EE and
CS University of California Berkeley
Gang Qu Electrical and Computer Engineering
Department University of Maryland
Miodrag Potkonjak Computer Science
Department University of California, Los Angeles
Presented by John Sweeney. Slides courtesy of
the author.
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Sensor Coverage

• Given
• Field A
• N sensors
• How well can the field be observed ?
• Closest Sensor (minimum distance) only
• Worst Case Coverage Maximal Breach Path
• Best Case Coverage Maximal Support Path
• Multiple Sensors speed and path considered
• Minimal Exposure Path

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Maximal Breach Path
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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Maximal Support Path

• 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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Exposure - Semantics

• Likelihood of detection by sensors function of
  time interval and distance from sensors.
• Minimal exposure paths indicate the worst case
  scenarios in a field
• Can be used as a metric for coverage
• Sensor detection coverage
• Wireless (RF) transmission coverage
• For RF transmission, exposure is a potential
  measure of quality of service along a specific
  path.

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Preliminaries Sensing Model
Sensing model S at an arbitrary point p for a
sensor s
where d(s,p) is the Euclidean distance between
the sensor s and the point p, and positive
constants ? and K are technology- and
environment-dependent parameters.
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Preliminaries Intensity Model(s)
Effective sensing intensity at point p in field F

All Sensors
Closest Sensor
K Closest Sensors K3 for Trilateration
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Definition Exposure
The Exposure for an object O in the sensor field
during the interval t1,t2 along the path p(t)
is
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Exposure Coverage Problem Formulation

• Given
• Field A
• N sensors
• Initial and final points I and F
• Problem
• Find the Minimal Exposure Path PminE in A,
  starting in I and ending in F.
• PminE is the path in A, along which the exposure
  is the smallest among all paths from I to F.

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Special Case One Sensor
Minimal exposure path for one sensor in a square
field
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General Exposure Computations

• Analytically intractable.
• Need efficient and scalable methods to
  approximate exposure integrals and search for
  Minimal Exposure Paths.

• Use a grid-based approach and numerical methods
  to approximate Exposure integrals.

• Use existing efficient graph search algorithms to
  find Minimal Exposure Paths.

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Minimal Exposure Path Algorithm

• Use a grid to approximate path exposures.
• The exposure (weight) along each edge of the grid
  approximated using numerical techniques.
• Use Dijkstras Single-Source Shortest Path
  Algorithm on the weighted graph (grid) to find
  the Minimal Exposure Path.
• Can also use Floyd-Warshall All-Pairs Shortest
  Paths Algorithm to find PminE between arbitrary
  start and end points.

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Generalized Grid
Generalized Grid 1st order, 2nd order, 3rd
order More movement freedom ? more accurate
results Approximation quality improves by
increasing grid divisionswith higher costs of
storage and run-time.
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Minimal Exposure Path Algorithm Complexity

• Single Source Shortest Path (Dijkstra)
• Each point is visited once in the worst case.
• For an nxn grid with m divisions per
  edgen2(2m-1)2nm1 total grid points.
• Worst case search O(n2m)
• Dominated by grid construction.
• 1GHz workstation with 256MB RAM requires less
  than 1 minute for n32, m8 grids.
• All-Pairs Shortest Paths (Floyd-Warshall)
• Has a average case complexity of O(p3).
• Dominated by the search O((n2m)3)
• Requires large data structures to store paths.

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PminE Uniform Random Deployment
Minimal exposure path for 50 randomly deployed
sensors using the All-Sensor intensity model (IA).
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Exposure Statistical Behavior
Diminishing relative standard deviation in
exposure for 1/d2 and 1/d4 sensor models.
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PminE Deterministic Deployment
Minimal exposure path under the All-Sensor
intensity model (IA) and deterministic sensor
deployment schemes.
Cross
Square
Triangle
Hexagon
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Exposure Research Directions

• Localized implementations
• Performance and cost studies subject to
• Wireless Protocols (MAC, routing, etc)
• Errors in measurements
• Locationing
• Sensing
• Numerical errors
• Computation based on incomplete information
• Not every node will know the exact position and
  information about all other nodes

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Summary

• Exposure
• Definition
• Efficient Algorithm
• Centralized Implementation
• Algorithm
• Generalized grid approximation
• Application of graph search algorithms
• Ad-hoc wireless sensor networks
• Coverage
• Quality of Service
• Research
• Numerous interesting open problems