Exposure In Wireless AdHoc Sensor Networks

1
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
2
Wireless Ad-Hoc Sensor Networks
GATEWAY
MAIN SERVER
CONTROL CENTER
3
Related Work

• Sensor Networks
• Communications of the ACM, vol. 43, May 2000.
• Proactive ComputingD. Tennenhouse.
• Embedding The Internet IntroductionD. Estrin,
  R. Govindan, J. Heidemann.
• Location Discovery
• ACM SIGMOBILE 2001 (same session)
• Dynamic Fine-Grained Localization in Ad-Hoc
  Networks of SensorsA. Savvides, C. Han, M.
  Srivastava
• Coverage
• Proceedings of IEEE Info COM, vol. 3, April 2001.
• Coverage Problems in Wireless Add-Hoc Sensor
  NetworksS. Meguerdichian, F. Koushanfar, M.
  Potkonjak, M. Srivastava

4
Exposure An Introduction
5
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.
6
Preliminaries Intensity Model(s)
Effective sensing intensity at point p in field F

All Sensors
Closest Sensor
K Closest Sensors K3 for Trilateration
7
Definition Exposure
The Exposure for an object O in the sensor field
during the interval t1,t2 along the path p(t)
is
8
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.

9
Special Case One Sensor
Minimal exposure path for one sensor in a square
field
10
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.

11
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.

12
Generic Exposure Problem

• Continuous Domain
• Solution
• Transform to a discrete domain
• Apply graph theory abstractions
• Calculate shortest path

13
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.
14
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.

15
PminE Uniform Random Deployment
Minimal exposure path for 50 randomly deployed
sensors using the All-Sensor intensity model (IA).
16
Exposure Statistical Behavior
Diminishing relative standard deviation in
exposure for 1/d2 and 1/d4 sensor models.
17
PminE Deterministic Deployment
Minimal exposure path under the All-Sensor
intensity model (IA) and deterministic sensor
deployment schemes.
Cross
Square
Triangle
Hexagon
18
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