1. Power Efficient Monitoring Management In Sensor Networks
Zelikovsky Georgia State
Joint work with
P. Berman Pennstate
G. Calinescu Illinois IT
Y. L i Georgia State
C. Shah Georgia State

2. Outline Sensor Network Model Maximum Sensor Network Lifetime Problem
Centralized Algorithms
Distributed Algorithms
Result
Conclusion

3. The set of sensors largely exceeds the necessary amount to monitor R
Sensor Network Model
All sensor nodes have the same sensing range r.
Each sensor monitor a disc region Ri
Each sensor has a battery life bi
The set of sensors largely exceeds the necessary amount to monitor R

4. Data Structure Grid Data Structure:
A set of grid points (gg) to discretize R.
Partition all grid points into ‘fields’.
A field is defined as a subset of grid points
covered by the same set of sensors.
New Data Structure:
Face: points covered by same set of sensors forms the equivalence class, called face.
Number of Intersection points are at most n(n-1)
Number of the faces o(n2)
Any face can not be covered partially.
face 1
face 8
face 7
face 6
face 11
face 2
face 3
face 4
face 5
face 10
face 9
face 12
face 13

5. Sensor Cover Problem And Sensor Lifetime Problem
Sensor cover - A set of sensors C covering monitored area R.
Generalized q-Cover q[0,1] problem,
e.g. q = 0.9, 90% monitored area covered by sensors.
For given constant q[0,1], the monitored region R with area M, and a set of sensors
Find subset {p1, p2, … , pt} of sensors.
such that  w (pi ) min
with the constraint
Partial q-Coverage problem is equivalent to the weighted set q-cover problem.
Sensor lifetime problem is a packing LP problem
LP formulation
Maximize:
Subject to:
CMij =
1 if sensor j covers face i
0 if sensor j doesn’t cover face j {
bi = lifetime of sensor i
tj a time variable for each cover cj.
Packing LP is defined as:
max{cTx| Ax ≤ b, x ≥ 0 }
— where A , b and c have positive entries;
— the dimensions of A as mn.

6. Maximizing the Sensor Network Lifetime Problem (SNLP)
Multiple sensor covers are found during the life time of the sensor networks
Disjoint set covers:
If any sensor in sensor-cover is died then new sensor cover is found
Every sensor participate in only one sensor cover
It gives life time of 2 unit for the scenario in fig.
Non-Disjoint set covers:
A sensor can participate in more than one sensor cover.
Time ti is given to sensor cover i
schedule ({p1, p2}, 1), ({p1 p3}, 1), ({p3, p2}), 1) gives the life time of 3 units P3
monitored
region R P2 P1
Each Sensor has 2 battery unit

7. Centralized Algorithmic solution for SNLP (Garg-Könemann / Tight / CPLEX )
Garg-Könemann finds the life time for each sensor cover and divides it by constant number based on epsilon and number of iteration
Tight solution is obtained using the finding the tightest energy constraint from Garg-Könemann solution
CPLEX
After Garg-Könemann finds the all the sensor-covers, the best time schedule for each sensor covers can be obtained using CPLEX
Constraints: satisfying the battery requirements
Objective: Maximizing the life time
Garg-Könemann is primal dual algorithm to solve the packing LP.
It finds the solution using iterations, which can be controlled by epsilon

8. Test Result (Life Time)
Number of Nodes
Sensing Range
Life Time GK
Tight
CPLEX
100
18.11
19.48
20.00
150
21.22
22.49
23.61
18.28
19.60
29.35
31.04
32.86
200
20.32
21.52
23.28
37.46
39.40
40.00
250
19.68
20.62
21.58
63.23
67.58
71.67
300
21.44
22.53
23.89
74.32
80.31
87.44
350
25.01
26.25
27.78
95.55
103.70
113.61
400
28.61
29.75
30.00
108.45
117.31
123.08

9. Test Result (Run Time) Number of Nodes Sensing Range Run Time GK Tight
CPLEX
100
3.55
5.06
12.39
150
5.75
7.58
17.87
6.86
9.63
23.09
17.55
21.52
43.31
200
13.26
17.10
42.26
45.83
53.00
90.98
250
20.74
25.81
57.03
120.21
135.88
228.48
300
34.11
40.70
81.49
220.28
242.91
382.78
350
53.37
62.60
118.40
459.39
495.52
765.16
400
79.40
91.67
161.27
795.01
841.47

10. Distributed Algorithms and State Diagram
Vulnerable sensors change it state into
--Active when there is a face which is not covered by any other active or vulnerable sensor
-- Idle state if all its faces are covered by one of two types of sensors: active or vulnerable sensors with a larger energy supply
Active/Idle sensors change its state into vulnerable state if any neighboring sensor becomes vulnerable. G
Permanent
Terminated
If there is a face not covered by any other active or vulnerable sensor
If all its faces are covered by active or vulnerable sensors with a larger energy supply
D or upon reaching the reshuffle-triggering threshold value
When neighbor node goes into vulnerable state
If current sensor is the only sensor covers one or more faces
F&G When sensor nodes exhausts all its batteries
Vulnerable E F A B
Active
Idle C D

11. Correctness of distributed algorithm
Theorem: The distributed algorithm always finds the minimal sensor cover.
Lemma: The distributed algorithm is deadlock-free.
Among vulnerable sensors there is always one that either should become active or idle
On the contrary, assume that each vulnerable sensor
covers at least one face non-covered by active sensor and
does not have an individual face
Then there is always vulnerable sensor which is not a champion for any of its faces:
Sensor 1 should be a champion for face say a, but a is not individual so there should be a sensor 2 covering face a and having less batteries than 1.
Similar, 2 is a champion for a face say b which is also covered by 3 who has less batteries than 2, and so on.
Since all the sensors 1,2, … have different battery supply, they all are different
Resulted active set is minimal since any active sensor has individual face
Resulted active set covers all faces since a sensor cannot go to idle state if it has individual face
Sensors 1 2 3 4 … n
Faces a b c d e

12. Reshuffle-Triggering Threshold Value
Number of Nodes
Sensing Range
Reshuffle-Triggering Threshold Value 1 2 3 5 10
100
19.33
18.67
18.33
15.00
10.00
150
21.67
21.33
20.00
18.00
17.67
16.67
31.33
30.00
28.33
25.00
23.33
200
20.33
39.33
38.67
37.33
35.00
33.33
250
19.67
13.33
67.67
64.67
63.33
60.00
50.00
300
81.67
78.00
75.33
70.00
350
26.67
25.33
108.33
104.00
100.33
93.33
80.00
400
29.33
28.67
118.00
114.00
112.00
106.67

13. New distributed algorithms
Consider the following case:
... … ….
Sensor with life time of 100
Face
Sensor with life time of 1
Optimum life time:
= 200
Life time by previous distributed algorithms:
Less than 102
Updated Algorithms: (Modified transition rules A and B in state diagram)
If it’s the only sensor cover the face
If not A and has the smallest battery energy among those which also cover the sink

14. Test Result Conclusion
For Maximizing the Sensor Network Lifetime Problem (MSNLP),
centralized and distributed algorithms are proposed and has been
compared in simulated environment
Centralized algorithms have trade-off between life time and run time
Distributed algorithms have trade-off between life time and
communication overhead