1. Barrier Coverage With Wireless Sensors
Santosh Kumar, Ten H. Lai and Anish Arora
Department of Computer Science and Engineering The Ohio State University
MobiCom 2005

2. Outline Introduction The network Model
Algorithm for k-Barrier coverage
Simulation
Conclusions

3. Introduction
Wireless sensor networks can replace such barriers

4. Introduction : Barrier Coverage
USA
Intruder

5. Introduction : Belt Region

6. The network model: Crossing Paths
A crossing path is a path that crosses the complete width of the belt region.
Crossing paths Not crossing paths

7. The network model: Two special belt regions
Rectangular:
Donut-shaped:

8. k-Covered
A crossing path is said to be k-covered if it intersects the sensing disks of at least k sensors.
3-covered covered covered

9. k-Barrier Covered
A belt region is k-barrier covered if all crossing paths are k-covered.
Not barrier covered
1-barrier covered

10. Barrier coverage vs. Blanket coverage
A belt region is k-barrier covered if all crossing paths are k-covered.
A region is k-blanket covered if all points are k-covered.
k-blanket covered k-barrier covered
1-barrier covered but
not 1-blanket covered

11. Algorithm for k-Barrier coverage:
Local? Global ?
Open Belt Region
Closed Belt Region
Optimal configuration for deterministic deployments
Min # sensors in random deployment

12. Algorithm for k-Barrier coverage: Non-locality of k-barrier Coverage

13. Algorithm for k-Barrier coverage: Non-locality of k-barrier Coverage

14. Open Belt Region Given a sensor network over a belt region
Construct a coverage graph G(V, E)
V: sensor nodes, plus two dummy nodes L, R
E: edge (u,v) if their sensing disks overlap
Region is k-barrier covered iff L and R are k-connected in G.

15. Open Belt Region R L

16. Closed Belt Region Coverage graph G
k-barrier covered iff G has k essential cycles (that loop around the entire belt region).

17. Closed Belt Region

18. Optimal Configuration for deterministic deployments
Assuming sensors can be placed at desired locations
What is the minimum number of sensors to achieve k-barrier coverage?
k x S / (2r) sensors, deployed in k rows r

19. Question ? If sensors are deployed randomly Desired are
How many sensors are needed to achieve k-barrier coverage with high probability (whp)?
Desired are
A sufficient condition to achieve barrier coverage whp
A sufficient condition for non-barrier coverage whp
Gap between the two conditions should be as small as possible

20. L(p) = all crossing paths congruent to p

21. Weak Barrier Coverage A belt region is k-barrier covered whp if
lim Pr(all crossing paths are k-covered) = 1 or
lim Pr( crossing paths p, L(p) is k-covered ) = 1
A belt region is weakly k-barrier covered whp if
crossing paths p, lim Pr( L(p) is k-covered ) = 1

22. Conjecture: critical condition for k-barrier coverage whp
Grid distribution with independent failures, Shakkottai03 (Infocom 2003)
c’(n) = npπr2/log(n)
If , then k-barrier covered whp
If , not k-barrier covered whp
Expected # of sensors in the
r-neighborhood of path s r
1/s

23. What if the limit equals 1?
Given:
Length (l), Width (w), Sensing Range (R), and Coverage Degree (k),
To determine # sensors (n) to deploy, compute
s2 = l/w
r = (R/w)*(1/s)
Compute the minimum value of n such that
2nr/s ≥ log(n) + (k-1) log log(n) + √log log(n) s

24. Simulations
Region of dimension 10km * 100m
Sensing radius 10m
P =0.1

25. Simulations Using this formula to determine n,
The n randomly deployed sensors provide weak k-barrier coverage with probability ≥0.99.
They also provide k-barrier coverage with probability close to 0.99.

26. Simulations

27. Conclusions Barrier coverage Basic results Open problems
Blanket coverage: extensively studied
Barrier coverage: still at its infantry

28. Thank you!