1. 報告者 : 吳雯僑 教授 : 陳仁暉 Mobile Computing

2. Grid Coverage for Surveillance and Target Location in Distributed Sensor Networks 作者 : Krishnendu Chakrabarty, Senior Member, IEEE, S. Sitharama Iyengar, Fellow, IEEE, Hairong Qi, Member, IEEE, and Eungchun Cho IEEE TRANSACTIONS ON COMPUTERS, DECEMBER 2002 What is Sensor? What is Sensor network?

3. what are we interested for? 1 Give different type of sensors and a surveillance region, determine the placement such that the sensor field is coveraged and cost is minimized.

4. what are we interested for? 2 how should the sensors be placed such that every grid point is covered by a unique subset of these sensors. A:[1,2,3] B:[1,2,6] C:[2] D:[5] E:[7] 4 3 2 1 5 6 Sensor 範圍 :1 步 A B C 78 D E =>D:[5,7] =>E:[5,7]

5. 1 Minimun Cost Sensor Placement ( 前提情要 ) 名詞介紹 1 Field : 三維空間 {X,Y,Z} consist of n x,n y,and n z grid points 2 Sensor type:{ A, cost=C A, range=R A B, cost=C B, range=R B } 3 grid point 的間距 : min{ R A,R B } 4 every grid pointmust be covered by at least m m =>amount of fault tolerance

6. 問題來了.. Given a parameter m >=1, a set of grid points, two types of sensors (Type A and Type B) with costs CA and CB, and ranges RA and RB, respectively, find an assignment of sensors to grid points such that every grid point is covered by at least m sensors and the total cost of the sensors is minimum.

7. 把問題寫成數學的模式 Let a ijk be a 0-1 variable define as follows a ijk ={ 1, if type Ａ sensor is placed at grid point (i,j,k) 0, otherwise } b ijk ={ 1, if type B sensor is placed at grid point (i,j,k) 0, otherwise } => C : total cost i=1j=1k=1 nxnx nyny nznz C= Σ Σ Σ ( C A a ijk +C B b ijk )

8. 把問題寫成數學的模式 Let cov A ((i1,j1,k1)(i2,j2,k2)) be a binary variable define as follows: cov A ((i1,j1,k1)(i2,j2,k2))= {1, if a type A sensor place at grid point (i1,j1,k1) covers grid point (i2,j2,k2) 0, otherwise } cov B,too i=1j=1k=1 nxnx nyny nznz C= Σ Σ Σ ( C A a ijk +C B b ijk ) i=1j=1k=1 nxnx nyny nznz Σ Σ Σ ( a i1j1k1 cov A ((i1,j1,k1)(i2,j2,k2)) +b ijk cov B ((i1,j1,k1)(i2,j2,k2)) )>=m 被幾個 Sensor A cover 被幾個 Sensor B cover => 1<=i2<=n x 1<=j2<=n y 1<=k2<=n z

9. Integer linear programming model for sensor placement

10. example

13. 2 Sensor Placement for Target Locatoin 想法 : based on the concept of identifying codes for uniquely identifying vertices in graphs 110 111 100 010 001 011 101 110 100 110 100

14. In Sensor networkIn Graph G Grid pointvertices Grid point where sensor placement Center of the ball (codeword) The unique location of a target by the sensor field The unique identification of a vertex in G

15. 定理 1 :denote the number of sensors required for uniquely identifying targets in an n-dimensional (n<=3) sensor field with p grid points in each dimension.

16. Some terminology For every grid point(x,y,z) in a sensor field,we associate aparity vector(px,py,pz),as follows: p x =x mod 2, p y =y mod 2, p z =z mod 2, for example : grid point (2,4,5) parity vector(0,0,1) grid point (1,2,3) parity vector(1,0,1) The set of parity vectors denote by p(c)

17. 定理 2 何謂 perfect binary(3,1,3)Hamming code?

18. Base on 定理 2 Example: let p=6. From Theorem 2, we see that sensors should be placed at the set of grid points {S0; S1}, where S0 and S1 are the set of grid points with parity vectors (0, 0, 0) and (1, 1, 1), respectively, as shown below:

19. 不懂 只要證明 B2 中所 含的點, 可以完全 被 B1 中的點唯一 決定, 就可得證 ?

20. Example Fig. 6. (a) An efficient placement of sensors given by Theorem 3. (b) An efficient ad hoc placement of sensors.

21. Conclusion 並非唯一解法 ? 是否有其他的解法 ? Need more study in detail!