Exposure In Wireless
Computer Science Department
University of California, Los Angeles
Farinaz Koushanfar Gang Qu Miodrag Potkonjak
Department of EE and CS Electrical and Computer Computer Science Department
University of California Engineering Department University of California
Berkeley University of Maryland Los Angeles
Wireless Ad-Hoc Sensor Networks
Wireless Ad-Hoc Sensor Networks
n Field A
n N sensors
How well can the field be observed ?
n Closest Sensor (minimum distance) only
n Worst Case Coverage: Maximal Breach Path
n Best Case Coverage: Maximal Support Path
n Multiple Sensors: speed and path considered
Minimal Exposure Path
n Related work
n Introduce Exposure
n Preliminaries and problem formulation
n Special cases
n Exposure calculation algorithm
n Experimental results
n Open problems and research directions
n Sensor Networks
Communications of the ACM, vol. 43, May 2000.
n Proactive Computing
n Embedding The Internet: Introduction
D. Estrin, R. Govindan, J. Heidemann.
n Location Discovery
ACM SIGMOBILE 2001 (same session)
n Dynamic Fine-Grained Localization in Ad-Hoc Networks of Sensors
A. Savvides, C. Han, M. Srivastava
Proceedings of IEEE Infocom, vol. 3, April 2001.
n Coverage Problems in Wireless Add-Hoc Sensor Networks
S. Meguerdichian, F. Koushanfar, M. Potkonjak, M. Srivastava
Exposure: An Introduction
Exposure - Semantics
n Likelihood of detection by sensors function
of time interval and distance from sensors.
n Minimal exposure paths indicate the worst
case scenarios in a field:
n Can be used as a metric for coverage
n Sensor detection coverage
n Wireless (RF) transmission coverage
RF transmission, exposure is a potential
measure of quality of service along a
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 l and K
are technology- and environment-dependent parameters.
Preliminaries: Intensity Model(s)
Effective sensing intensity at point p in field F :
K Closest Sensors
K=3 for Trilateration
The Exposure for an object O in the sensor
field during the interval [t1,t2] along the path
Exposure – Coverage Problem Formulation
n Field A
n N sensors
n Initial and final points I and F
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.
Special Case – One Sensor
Minimal exposure path for one sensor in a square field:
General Exposure Computations
n Analytically intractable.
n Need efficient and scalable methods to
approximate exposure integrals and search for
Minimal Exposure Paths.
n Use a grid-based approach and numerical
methods to approximate Exposure integrals.
n Use existing efficient graph search
algorithms to find Minimal Exposure Paths.
Minimal Exposure Path Algorithm
n Use a grid to approximate path exposures.
n The exposure (weight) along each edge of the
grid approximated using numerical techniques.
n Use Dijkstra’s Single-Source Shortest Path
Algorithm on the weighted graph (grid) to find
the Minimal Exposure Path.
n Can also use Floyd-Warshall All-Pairs Shortest
Paths Algorithm to find PminE between arbitrary
start and end points.
Rectilinear Grids – Not Good Enough
Square Equilateral Triangle
Black = Red = Yellow = Blue
Length Red = Length Blue = 2 x Green = 2 x L
Generalized Grid – 1st order, 2nd order, 3rd order …
More movement freedom à more accurate results
Approximation quality improves by increasing grid divisions
with higher costs of storage and run-time.
Minimal Exposure Path Algorithm Complexity
n Single Source Shortest Path (Dijkstra)
n Each point is visited once in the worst case.
n For an nxn grid with m divisions per edge:
n2(2m-1)+2nm+1 total grid points.
n Worst case search: O(n2m)
n Dominated by grid construction.
n 1GHz workstation with 256MB RAM requires less than
1 minute for n=32, m=8 grids.
n All-Pairs Shortest Paths (Floyd-Warshall)
n Has a average case complexity of O(p3).
n Dominated by the search: O((n2m)3)
n Requires large data structures to store paths.
PminE – Uniform Random Deployment
Minimal exposure path for 50 randomly deployed sensors
using the All-Sensor intensity model (IA).
8x8 m=1 16x16 m=2 32x32 m=8
Exposure: 0.7079 Exposure: 0.6976 Exposure: 0.6945
Length: 1633.9 Length: 1607.7 Length: 1581.0
Exposure – Statistical Behavior
Diminishing relative standard deviation in exposure
for 1/d2 and 1/d4 sensor models.
PminE – Deterministic Deployment
Minimal exposure path under the All-Sensor intensity model
(IA) and deterministic sensor deployment schemes.
Cross Square Triangle Hexagon
Sensors Cross Triangle Hexagon
Exposure Level ~20 6x 3x 1.5x
(compared to Square) ~120 30x 1.5x 1.5x
Exposure – Research Directions
n Performance and cost studies subject to
n Wireless Protocols (MAC, routing, etc)
n Errors in measurements
n Numerical errors
n Computation based on incomplete information
n Not every node will know the exact position and
information about all other nodes
n Efficient Algorithm
n Centralized Implementation
n Generalized grid approximation
n Application of graph search algorithms
n Ad-hoc wireless sensor networks:
n Quality of Service
n Numerous interesting open problems