1. 1 Power Efficient Monitoring Management in Sensor Networks A.Zelikovsky Georgia State joint work with P. BermanPennstate G. Calinescu Illinois IT C. Shah Georgia State

2. 2 Outline Maximum sensor network lifetime Monitoring model in sensor networks Disjoint vs Nondisjoint sensor covers Example of MAX-SNLP Minimum weigh sensor cover Garg-Konemann algorithm LP enhancement of GK Distributed Algorithms Experimental results Conclusions

3. 3 Sensor Networks Model Sensor Region L Monitor Region R Randomly Deployed Sensors over L  The set of sensors largely exceeds the necessary amount to monitor R

4. 4  A formal definition of the energy preserving scheduling problem Maximum Sensor Network Lifetime Problem Sensor cover : A set of sensors C covering R. A monitoring schedule: a set of pairs (C 1, t 1 ),…, (C k,t k ). — C i is a sensor cover; — t i is time during which C i is active.  Maximum Sensor Network Lifetime problem Given: a monitored region R, a set of sensors p 1, …, p n, and monitored region R i,and energy supply b i for each sensor Find: a monitoring schedule (C 1,t 1 ), …, (C k, t k ) with the maximum length t 1 + … + t k, such that for any sensor p i the total active time does not exceed b i.

5. 5  Previous work assumed that sensor covers are disjoint Disjoint vs Nondisjoint Sensor Covers Slijepcevic and Potkonjak [01], Cardei and Du [03], Zussman and Segall [03] This is unnecessary constraint: the lifetime can be prolonged if we do not use each sensor cover till battery exhaustion but switch to another one.  An example ( Disjoint vs. Non-disjoint set covers). It shows advantage of switching between sensor covers. Example Properties Any sensor is assumed to have 2 batteries Any sensor alone cannot cover R Any two sensors cover R Disjoint sensor covers formulation: Any two sensor covers intersect — There is one single disjoint sensor cover; — The total lifetime of schedule is 2 units of time. monitored region R sensor regions R1R1 R2R2 R3R3

6. 6 Example of Maximum Sensor Network Lifetime Problem  Advantage of switching between sensor covers: Non-disjoint set covers: — the schedule ({p 1, p 2 }, 1), ({p 2 p 3 }, 1), ({p 3, p 1 }), 1); — 3 units of time. R1R1 R2R2 R3R3 monitored region R R1R1 R2R2 R3R3 monitored region R R1R1 R2R2 R3R3 sensors p1 and p2 for 1 time unit sensors p1 and p3 for 1 time unit sensors p2 and p3 for 1 time unit monitored region R

7. 7 Maximum Sensor Network Lifetime Problem (cont’d)  Primal /dual approach: uses solution for the dual problem for solving primal problem  The Dual Problem: Minimum weight sensor cover problem Given a monitored region R, a set of sensors p 1,…,p n and monitored region R i and the weight w i for each sensor; Find sensor cover with the minimum total weight.  Disc Cover selection  Garg-Konemann algorithm

8. 8 Grid Data Structure Representing Sensor Coverage  Grid data structure (Used by Potkonjak and Slijepcevic) 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. Advantage — easy to implement — good if coverage delineation does not need to be very precise. Disadvantages — if too few grid points: coverage of the area not well defined. — if too many grid points: large calculation Time = Ω(n*g 2 ) A grid of g  g

9. 9 Data Structure face 1 face 8 face 7 face 6 face 11 face 2 face 3face 4 face 5 face 10 face 9 face 12 face 13 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(n 2 ) Any face can not be covered partially.

10. 10  Comparison of planar graph and grid data structures Experimental Results

11. 11 Greedy Heuristics Greedy heuristics is used to find the sensor cover. For partial q-cover problem, solution can be approximated with (1 + ln (1-q) -1 )

12. 12  LP formulation Maximize : Subject to : — CM ij = 1 if sensor j covers face i 0 if sensor j doesn’t cover face j { — b i = lifetime of sensor i — t j a time variable for each cover c j.  Packing LP is defined as: max{c T x| Ax ≤ b, x ≥ 0 } — where A, b and c have positive entries; — the dimensions of A as m  n.  Sensor lifetime problem is a packing LP problem MSNLP

13. 13 Garg-Könemann Algorithm Garg-Könemann is primal dual algorithm to solve the packing LP. It finds the solution using iterations, which can be controlled by epsilon

14. 14 State diagram of GK algorithm A weight is assigned to the each sensor according to the batteries it has Find the weighted q-set cover Garg-Könemann algorithm 1.Finds the life time for the q-set cover based on bottleneck sensor 2.Increases the weight of node based on i.Epsilon ( quality of the Garg-Könemann) ii.Batteries left 3.Change dual variables Condition for exit is checked based on dual variables

15. 15 Tight & CPLEX Tight  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

16. 16  GK Algorithm and LP enhancement LP Enhancement vs GK * The lesser the , the accuracy of GK,  the more sensor covers are found  the more runtime  the better quality of the approximate solution * CPLEX improves significantly over the Garg-Konemann. No. of Sensors Rang e  GKCPLEX LifetimeRunning time (Sec) LifetimeRunning time (Sec) 100 0.5015.781.24300.02 100 0.1027.152.69300.12 100 0.0528.547.32300.56 1002000.5045.326.63830.06 1002000.1073.7525.19920.89 1002000.0536.6733.91430.41 1003000.50108.0314.852230.09 2001000.5028.089.75510.11 2001000.1048.9322.45566.90 200 0.50101.3043.101700.04 200 0.10156.99262.911700.50 2003000.50222.50141.934090.13 5001000.5073.50152.931290.62 10001000.50148.861179.6328333.43

17. 17 Simulation Parameters Sensor Area1000m x 1000m Monitored Area800m x 800m Epsilon (Decides quality of GK)0.1 Number of Nodes100, 150, 200, 250, 300, 350, 400 Sensing (Monitoring) Range100m and 150m Partial (q) coverage1 (100%) and 0.9 (90%) Battery Assignment10, and randomly between 10 and 20 Reshuffle-Trigger1,2,3,5 and 10

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20. 20 Distributed Algorithms Assumptions  Sensor nodes only know about the neighbors information (e.g. batteries left, current state and id) on receiving information packets  Neighbors of node N can be defined as set of nodes sharing the faces with node N Communication range = 2 * monitoring range  Node can sleep (not monitor the region), but it always listens to the neighbors

21. 21 State diagram to find the sensor cover Vulnerable IdleActive A D C B We first put all the nodes in vulnerable state A.If there is a face which is not covered by any other active or vulnerable sensor, then go to active state and inform neighbors B.if all its faces are covered by one of two types of sensors: active or vulnerable sensors with a larger energy supply, i.e., the sensor is not a champion for any of its faces, then go to idle state and inform neighbors

22. 22 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 1 a 234n bcde Sensors Faces …

23. 23 Life time in the distributed algorithms  As described in centralized algorithms, we need to shuffle sensor covers to maximize the lifetime of the sensor networks  After sensor node goes to Active state, it will stay in Active state for pre- defined time called Reshuffle-triggering threshold value. Upon reaching the threshold value, node in Active state will go to Vulnerable state and inform the neighbors If sensor node is in Idle or Active state then it will go in vulnerable state, if one of its neighbor goes into Vulnerable state It causes global reshuffle and it will find new minimal sensor cover  There is a trade-off between quality of the life time and number of reshuffles

24. 24 State diagram for lifetime Vulnerable IdleActive A D C B C.1. Upon reaching the reshuffle-triggering threshold value 2. When neighbor node goes in vulnerable state D.2. When neighbor node goes in Vulnerable state

25. 25 State diagram with Permanent and Dead V IdleActive A DC B E.If current sensor is the only sensor which covers one or more faces F&G.When sensor nodes exhausts all its batteries Permanent Solution: Node in vulnerable state directly goes to the Permanent (no- reshuffle, no active state) state, similar to disjoint sensor cover problem Permanent Dead E G F

26. 26 Results Result of centralized algorithms Results of distributed algorithms  Show the comparison between Life time and Communication overhead for the distributed algorithms with different reshuffle- triggering threshold values Comparison of distributed algorithms with centralized algorithms

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29. 29 Results Result of centralized algorithms Results of distributed algorithms Comparison of distributed algorithms with centralized algorithms  The lifetime of the different distributed algorithms are compared with centralized algorithms (GK, Tight and CPLEX)

30. 30 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 q-Cover Problem

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33. 33 Conclusions In Sensor Networks,  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