1. Connectivity and Scheduling in Wireless Sensor Networks
Youn-Hee Han
Korea University of Technology and Education Internet Computing Laboratory

2. Connectivity

3. Connectivity Why Connectivity?
Any sensing data should be sent to gateway (sink, base station) node
Multi-hop routing
Base Station
Sink

4. K-Connectivity Connected Graph of Sensor Networks
Vertex: each sensor nodes
Edge: direct communication path for pairs of sensors
there exists an edge between two vertices iff the distance between them is less or equal to the transmission range r.

5. K-Connectivity [Definition] k-connectivity
The network will remain connected after removing any arbitrary k-1 sensors from network.
It is also called “vertex k-connectivity” (not “edge k-connectivity”)
k-connected:  any pair of nodes are connected by k indep. paths
Independent paths:

6. K-Connectivity
Examples
2-connected
4-connected

7. K-Edge-Connectivity [Definition] k-edge-connectivity
The network will remain connected after removing any arbitrary k-1 edges from network.
k-edge-connected:  any pair of nodes are connected by k disjoint paths
disjoint paths:

8. Min-Power Connectivity Problem
Connectivity & Transmission Power
Nodes in the network correspond to transmitters
More power  larger transmission range  More Edges  More Connectivity
transmitting to distance r requires r power
Battery operated  power conservation critical
[Definition] Min-Power Connectivity Problems
Find min-power range assignment so that the resulting communication network satisfies prescribed properties (k-connectivity)

9. Min-Power Connectivity Problema c d g f e a b d g f e c
Range assignment
Communication network

10. K-Connectivity & K-Coverage
Relation between K-Coverage and K-Connectivity [3]
Communication Range:
Sensing Range:
[Theorem]
If the given region is continuous and , “The region is k-covered” means “The region is k-connected”
For example, k=1
Assume that the requested coverage level, k, is one and
If The sensors covers the whole region completely, then
Any sensing data produced by a sensor can be delivered to the sink node.

11. Sensing and Communication Ranges
Real Products’ Ranges [7]

12. Coverage and Surveillance Path
[Voronoi Diagram Tutorial]

13. Voronoi diagram Voronoi diagram [8]
The Voronoi diagram is formed from lines that bisect and are perpendicular to the lines that connect two neighboring sensors.
Each point s has a Voronoi cell V(s) consisting of all points closer to s than to any other point

14. Voronoi diagram Voronoi diagram examples 1 point
2 points form “a perpendicular bisector”

15. Voronoi diagram Voronoi diagram examples
Collinear points form “a series of parallel lines”

16. Voronoi diagram Voronoi diagram examples
Non-collinear points form “Voronoi half lines” that meet at a vertex

17. Voronoi diagram Voronoi cells and segments
Which of the following is true for 2-D Voronoi diagrams?
Four or more non-collinear pointss are… 1) sufficient to create a bounded cell 2) necessary to create a bounded cell 3) 1 and 2 4) none of above
Four points’ degenerate case of bounded cell:

18. Property I of Voronoi diagram

19. Property II of Voronoi diagram

20. Surveillance Path Maximal Breach Path [8]
Voronoi Path (= Maximal Breach Path)
The path where the surveillance level is the lowest
The path where its closest distance to any sensor is as large as possible.
Voronoi Path (Edge)
Voronoi diagram
Voronoi Partition

21. Surveillance Path Maximal Support Path [8]
Delaunay Triangulation Path (= Maximal Support Path)
The path where the surveillance level is the lowest
The path where its closest distance to any sensor is as short as possible.
Delaunay triangulation

22. Coverage and Scheduling

23. Scheduling Basic Policy Sensor should be active or sleep?
Scheduling (related to the coverage issue)
An interval: is active
Another interval: is active
So, the battery power can be saved

24. Scheduling Scheduling Type Centralized Distributed
All sensors send “their location information” to the centralized sink node.
The sink node performs “its scheduling algorithm” for the sensors
The sink node broadcasts “the scheduling information” to all sensor nodes
Each sensor becomes active or sleep according to the information
Distributed
Each sensor self-determies its scheduling time
# of messages reduced

25. Centralized Scheduling
MDSC (Maximum Disjoint Set Covers) [9]
[Definition] Maximum Disjoint Set Covers Problem

26. Centralized Scheduling
MDSC (Maximum Disjoint Set Covers) [9]
For example,
C={S1, S2, S3, S4}, TARGETS={t1, t2, t3}
A sensor’s battery lifetime: 1
Network Lifetime without any scheduling: 1
By MDSC Scheduling
Two Set Covers, C1 and C2
C1={S1, S2} with active time=1
C1={S3, S4} with active time=1
So that, network lifetime: 2 s2 s1 s4 s3 t3 t1 t2 s1 s2 s3 s4 t3 t2 t1

27. Centralized Scheduling
MSC (Maximum Set Covers) [10]
[Definition] Maximum Set Covers Problem
removed!
MSC
MDSC
MDSC problem is a special case of MSC problem.!

28. Centralized Scheduling
MSC (Maximum Set Covers) [10]
For Example,
By MSC Scheduling
Network Lifetime: 2.5 s2 s1 s4 s3 t3 t1 t2
active time=0.5
active time=0.5
active time=0.5
active time=1

29. Centralized Scheduling
Integer Programming Formulation of the MSC Problem [10]

30. Centralized Scheduling
Integer Programming Formulation of the MSC Problem [10]

31. Centralized Scheduling
Integer Programming  Linear Programming

32. Centralized Scheduling
MSC (Maximum Set Covers) [10, 11]
Existing Algorithms
Linear Programming [10]
Greedy [10] (Complexity: )
Branch-and-Bound [11]
i: # of set covers, m: # of targets, n: # of sensors

33. Centralized Scheduling
MSC (Maximum Set Covers) [10, 11]
Existing Algorithms
Linear Programming [10]
Greedy [10] (Complexity: )
Branch-and-Bound [11]
i: # of set covers, m: # of targets, n: # of sensors

34. Distributed Scheduling
1-Coverage Preserving Scheduling (1-CP) [12]
For Example
Init Phase: 1) Each sensor exchange its location and Ref. value
2) Each sensor get its schedule (active) time
The set of intersection points within ‘s area
Trnd=20
The set of sensors covering the target p
Ref1=2, Ref2=9, Ref3=11

35. Distributed Scheduling
1-Coverage Preserving Scheduling (1-CP) [12] 2
16.5
5.5 11 9

36. References
C.-F. Huang and Y.-C. Tseng, The Coverage Problem in a Wireless Sensor Network, In ACM International Workshop on Wireless Sensor Networks and Applications (WSNA), pp. 115–121, 2003.
N. Ahmed, S. S. Kanhere and S. Jha, Probabilistic Coverage in Wireless Sensor Networks, in Proceedings of the IEEE Workshop on Wireless Local Networks (WLN, in conjunction with LCN 2005) , Sydney, Australia, pp , November 2005.
X. Wang, G. Xing, Y. Zhang, C. Lu, R. Pless, and C. Gill, Integrated coverage and connectivity configuration in wireless sensor networks, In ACM International Conf. on Embedded Networked Sensor Systems (SenSys), pp. 28–39, 2003.
C.-F. Huang, Y.-C. Tseng, and L.-C. Lo, The Coverage Problem in Three-Dimensional Wireless Sensor Networks, Journal of Interconnection Networks, Vol. 8, No. 3, pp Sep
Y. Zou and K. Chakrabarty, "Sensor deployment and target localization based on virtual forces," in Proceedings of INFOCOM 2003, March 2003.
S.-P. Kuo, Y.-C. Tseng, F.-J. Wu, and C.-Y. Lin, A Probabilistic Signal-Strength-Based Evaluation Methodology for Sensor Network Deployment, International Journal of Ad Hoc and Ubiquitous Computing, Vol. 1, No. 1-2, pp. 3-12, 2005
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37. References
Honghai Zhang and Jennifer C. Hou, ``On deriving the upper bound of a-lifetime for large sensor networks,'' Proc. ACM Mobihoc 2004, June 2004
S. Megerian, F. Koushanfar, G. Qu, G. Veltri, M. Potkonjak. "Exposure In Wireless Sensor Networks: Theory And Practical Solutions," Journal of Wireless Networks, Vol. 8, No. 5, ACM Kluwer Academic Publishers, pp , September 2002
M. Cardei and D.-Z. Du, "Improving Wireless Sensor Network Lifetime through Power Aware Organization," ACM Wireless Networks, Vol. 11, pp , 2005.
M. Cardei, M. T. Thai, Y. Li, and W. Wu, "Energy-efficient Target Coverage in Wireless Sensor Networks," In IEEE Infocom 2005, vol. 3, pp , 2005.
김용환, 이헌종, 한연희, "무선 센서 네트워크 수명 연장을 위한 에너지 인지적 스케줄링 알고리즘," 한국정보과학회 학술발표논문집 2008년도 가을, 2008년 10월
C.-F. Huang, L.-C. Lo, Y.-C. Tseng, and W.-T. Chen Decentralized Energy-Conserving and Coverage-Preserving Protocols for Wireless Sensor Networks, ACM Trans. on Sensor Networks, Vol. 2, No. 2, pp , 2006.
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