1. Secure Scheduling for Barrier Coverage
Ding-Zhu Du
University of Texas at Dallas

2. Outline Background Our Research Future
Brief overview of social networks
How to build applications on top of the social network
–  Think about a social network being MS Windows, We can build applications on it.

3. Background

4. Sink Internet / Satellite Sensor network
Sensing Area
phenomenon
User1
Sink
Internet / Satellite
Sensor network
User2

5. Biological
Systems

6. intruder
Area of interest

7. Open belt
Closed belt

8. Barrier Cover A barrier-cover is a set of sensors covering
a curve connecting two open boundaries.

9. Homogeneous Sensor Network
All sensors have the same size of sensing disks,
the same size of communication disks, and the
same lifetime, say unit time lifetime.

11. There may exist several barrier covers.

12. Sleep-wakeup scheduling may increase the lifetime of barrier coverage.
But, there is a security problem!

13. There is a breach in scheduling (B2, B1)

14. There is a breach in scheduling (B2, B1)
intruder a B2

15. There is a breach in scheduling (B2, B1)
intruder

16. There is no breach in scheduling (B1, B2)

17. Both (B2, B1) and (B1,B2) contain a breach.
Crossing is bad!

18. Donghyun Kim, Hyunbum Kim, Deying Li, Sung-Sik Kwon, Alade O
Donghyun Kim, Hyunbum Kim, Deying Li, Sung-Sik Kwon, Alade O. Tokuta, and Jorge A. Cobb, "Maximum Lifetime Dependable Barrier-coverage in Wireless Sensor Networks," Ad Hoc Networks (ADHOC), vol. 36, issue P1, pp , January 2016.
This paper gave 3 approaches to removing crossing by delete some barrier-covers.

19. Our Research

20. Observation Removal crossing is sufficient, but not necessary!
(B3,B2,B1) is a breach-free scheduling.

21. Starting with following Goals
Goal 1: Find necessary and sufficient condition for a sleep-wakeup scheduling to be breach-free.
Goal 2: Given a set of barrier-covers, find a maximum subset with breach-free scheduling. (complexity & Algorithm)

22. We completely reached goals
1 Give necessary and sufficient condition for a sleep-wakeup scheduling to be breach-free.
2 Given a set of barrier-covers, find a maximum subset with breach-free scheduling. (This problem is equivalent to the longest path problem in directed graph. )
3 Heterogeneous sensor system

23. Necessary and Sufficient1

24. Sleep-wakeup scheduling2
How to find?
Step 1. Using the necessary and sufficient condition,
construct a breach-free digraph.
Step 2. Find the longest path in the beach-free
digraph.

25. B1 B2 B3
Breach Digraph
Breach-free Digraph

26. (B3,B2,B1) is a breach-free scheduling.

27. Equivalence

28. Fig. 6

31. Corollary
The longest path problem

32. Longest Path

33. Heterogeneous Sensors3

35. Path Decomposition

36. sleep-wakeup scheduling
The longest path problem

37. Node-weight  edge weight

39. Recall
Find max flow.
Decompose flow into path-flows. Each path-flow gives a barrier-cover with lifetime (=flow value).
Find a max-lifetime subset of barrier-covers with a breach-free scheduling.

40. Questions
Is decomposition unique? If not, how to give the best decomposition?
Does max flow give a solution with longest lifetime breach-free scheduling?

41. Thanks, End