1. Coverage Preserving Redundancy Elimination in Sensor Networks Bogdan Carbunar, Ananth Grama, Jan Vitek Computer Sciences Department Purdue University West Lafayette, IN 47907, USA IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks (SECON ’ 04)

2. Outline  Introduction  Distributed detection of redundant sensors  Management of redundant sensors  Simulation  Conclusion

3. Introduction  Energy is a paramount concern in wireless sensor network Applications need to operate for a lone time  This paper focuses on Detect redundant sensors  Voronoi diagram Select maximum number of redundant sensors that can safely turn off simultaneously

4. Introduction SiSi SjSj SkSk SmSm S m is a redundant sensor SlSl

5. Introduction  Voronoi diagram Sites S 1, S 2, …, S n in the plane Divide the plan into n cells Any point in the cell are closest to only one site

6. Introduction  Voronoi diagram Voronoi edge Voronoi vertex Voronoi cell

7. Distributed detection of redundant sensors  Assumption All sensors have the same sensing range Each sensor knows its location information

8. Distributed detection of redundant sensors  The Voronoi generator of S are A, B, C, D A B D S C Voronoi Cell E

9. Distributed detection of redundant sensors  Lemma: The Voronoi generators of a sensor S, G s, are the ones closest to S A B D S C E

10. Distributed detection of redundant sensors  Lemma: The Voronoi generators of a sensor S, G s, are the ones closest to S A B D S C E

11. Distributed detection of redundant sensors  Lemma: The Voronoi generators of a sensor S, G s, are the ones closest to S S1 a b c S2 S3 e v dist (b, e)=dist (b, v) +dist (v, e) =dist (b, v) +dist (S3,v) >dist (S3, b)=r dist (S2, a)=dist (S2,b)=r dist (S3, c)=dist (S3,b)=r Another sensor can only be placed in the hashed area

12. Distributed detection of redundant sensors  Lemma: The Voronoi generators of a sensor S, G s, are the ones closest to S S1 a b c S2 S3 e v Any sensor placed in the hashed area covers less of S1 ’ s coverage area than S2 and S3 S4 If S1 is a redundant sensor, we infer that S1 is completely covered by the Voronoi generators of S1

13. Distributed detection of redundant sensors  Lemma: The Voronoi generators of a sensor S, G s, are the ones closest to S S1S1 S2S2 S3S3 V

14. Distributed detection of redundant sensors  Definition : The 2-Voronoi diagram of a sensor S A B D S C 2-Voronoi Vertices (2-VV) 2-Voroni Intersection Point (2-VIP) 2-Voronoi Edge (2-VE)

15. Distributed detection of redundant sensors  Theorem: A sensor S is redundant if and only if all the 2- VVs and 2-VIPs of S are covered by the Voronoi generators of S A B D S C 2-Voronoi Vertices (2-VV) 2-Voroni Intersection Point (2-VIP)

16. Distributed detection of redundant sensors  Theorem: A sensor S is redundant if and only if all the 2- VVs and 2-VIPs of S are covered by the Voronoi generators of S A B D S C

17. Distributed detection of redundant sensors  Theorem: A sensor S is redundant if and only if all the 2- VVs and 2-VIPs of S are covered by the Voronoi generators of S A B S C

18. Distributed detection of redundant sensors  Theorem: A sensor S is redundant if and only if all the 2- VVs and 2-VIPs of S are covered by the Voronoi generators of S A B S C

19. Management of redundant sensors  Blind Points

20. Management of redundant sensors  Blind Points Blind Point

21. Management of redundant sensors  G R =(V R, E R ) G R is the redundant graph V R is the set of redundant sensors E R is between two redundant sensors if and only if they are Voronoi neighbors abcde f g Send a message 1.ID 2.Number of it redundant Voronoi generator 12321 2 1

22. Management of redundant sensors  G R =(V R, E R ) G R is the redundant graph V R is the set of redundant sensors E R is between two redundant sensors if and only if they are Voronoi neighbors abcde f g 1232 2 1 1 A sensor that has the smallest value is a winner Each redundant sensor compares it value with the values received

23. Management of redundant sensors  G R =(V R, E R ) G R is the redundant graph V R is the set of redundant sensors E R is between two redundant sensors if and only if they are Voronoi neighbors abcde f g 1232 2 1 1 A winner sends a message stating that it is winner

24. Simulation  1000x1000 m 2  We randomly generate 10 different sensor network configurations

25. Simulation All the sensors have the same sensing range 50m

26. Simulation Sensing Range

27. Conclusion  This paper propose an efficient distributed algorithm for the coverage-preserving, energy-efficient redundant elimination problem Reduce overall system energy consumption Increase network system lifetime