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Mobile Computing

Mobile Computing. 報告者 : 吳雯僑 教授 : 陳仁暉. Grid Coverage for Surveillance and Target Location in Distributed Sensor Networks. What is Sensor?. 作者 : Krishnendu Chakrabarty, Senior Member, IEEE, S. Sitharama Iyengar, Fellow, IEEE, Hairong Qi, Member, IEEE, and Eungchun Cho

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Mobile Computing

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  1. Mobile Computing 報告者:吳雯僑 教授:陳仁暉

  2. Grid Coverage for Surveillance and TargetLocation in Distributed Sensor Networks What is Sensor? 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 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] A 1 3 C B 2 4 =>D:[5,7] =>E:[5,7] D 5 6 7 E 8 Sensor 範圍:1步

  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 nx,ny,and nz grid points 2 Sensor type:{ A , cost=CA, range=RA B , cost=CB, range=RB } 3 grid point的間距 : min{ RA,RB} 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. nx ny nz C= ΣΣΣ ( CAaijk+CBbijk) i=1 j=1 k=1 把問題寫成數學的模式 Let aijk be a 0-1 variable define as follows aijk={ 1, if type Ａ sensor is placed at grid point (i,j,k) 0, otherwise } bijk={ 1, if type B sensor is placed at grid point (i,j,k) 0, otherwise } => C : total cost

  8. nx nx ny ny nz nz ΣΣΣ ( ai1j1k1covA((i1,j1,k1)(i2,j2,k2)) +bijkcovB((i1,j1,k1)(i2,j2,k2)) )>=m C= ΣΣΣ ( CAaijk+CBbijk) i=1 i=1 j=1 j=1 k=1 k=1 把問題寫成數學的模式 • Let covA((i1,j1,k1)(i2,j2,k2)) be a binary variable define as follows: • covA((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 } • covB,too 1<=i2<=nx 1<=j2<=ny 1<=k2<=nz => 被幾個Sensor B cover 被幾個Sensor A cover

  9. Integer linear programming model for sensor placement

  10. example

  11. example

  12. 2 Sensor Placement for Target Locatoin • 想法: based on the concept of identifying codes for uniquely identifying vertices in graphs 101 100 100 100 111 110 110 110 001 010 011

  13. 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.

  14. Some terminology • For every grid point(x,y,z) in a sensor field ,we associate aparity vector(px,py,pz),as follows: px=x mod 2, py=y mod 2, pz=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)

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

  16. 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:

  17. 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?

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

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

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