Harbin Institute of Technology Application-Aware Data Collection in Wireless Sensor Networks Fang Xiaolin Harbin Institute of Technology

2 Outline n Existing work n Our problem n An approximation algorithm n An special instance n Simulations

3 Harbin Institute of Technology Existing work n Multi-application based data collection Data sharing [9] Sample as less data as possible Data point Existing work studies data point sampling

4 Harbin Institute of Technology Our problem n Multi-application based data collection n Sample data for a continuous interval Acoustic, video information [10], [11] Vibration measurement [12], [13], [14] Speed information [15] Sample an interval

5 Harbin Institute of Technology Problem definition Given a set of n tasks T, each task Ti is denoted as Ti = bi: beginning time ei: end time li: data sampling interval length Find a continuous sub-interval Ii for each task Ti so that

6 Harbin Institute of Technology Problem complexity n Non-linear non-convex optimization problem Nonlinear integer programming problem, If bi,ei,li are regarded as integers

7 Harbin Institute of Technology Greedy algorithm overview n 1. Sort by end times n 2. Find task set P overlap with first n 3. Find solution for P, and Remove n 4. Back to step 2

8 Harbin Institute of Technology Greedy algorithm overview n 1. Sort by end times n 2. Find task set P overlap with first n 3. Find solution for P, and Remove n 4. Back to step 2

9 Harbin Institute of Technology Greedy algorithm overview n 1. Sort by end times n 2. Find task set P overlap with first n 3. Find solution for P, and Remove n 4. Back to step 2

10 Harbin Institute of Technology Greedy algorithm overview n 1. Sort by end times n 2. Find task set P overlap with first n 3. Find solution for P, and Remove n 4. Back to step 2

11 Harbin Institute of Technology Find solution for P n Compute [s,e] for the tasks overlap with each other

12 Harbin Institute of Technology Approximation algorithm analysis n Approximation ratio is 2 n Time complexity is

13 Harbin Institute of Technology A special instance General problem Ti = Special instance Ti = n The data length is the same Can be solved in O(n 2 )

14 Harbin Institute of Technology Algorithm overview n1n1. Sort by the end times n2n2. Remove tasks cover other tasks n3n3. Dynamic programming Does not affect the result

15 Harbin Institute of Technology Algorithm overview n 1. Sort by the end times n 2. Remove tasks cover other tasks n 3. Dynamic programming

16 Harbin Institute of Technology Algorithm overview n 1. Sort by the end times n 2. Remove tasks cover other tasks n 3. Dynamic programming Computing x(i,j), then x(1,n) is the result [3,7] [5,9] [12,16] x(i,j)[s,e] x(1,1)[3,7] x(2,2)[5,9] x(3,3)[12,16] x(1,2)[3,8] x(2,3)[5,10]

17 Harbin Institute of Technology Algorithm overview n 1. Sort by the end times n 2. Remove tasks cover other tasks n 3. Dynamic programming Computing x(i,j), then x(1,n) is the result [3,8] x(i,j)[s,e] x(1,1)[3,7] x(2,2)[5,9] x(3,3)[12,16] x(1,2)[3,8] x(2,3)[5,10]

18 Harbin Institute of Technology Algorithm overview n 1. Sort by the end times n 2. Remove tasks cover other tasks n 3. Dynamic programming Computing x(i,j), then x(1,n) is the result [5,10] x(i,j)[s,e] x(1,1)[3,7] x(2,2)[5,9] x(3,3)[12,16] x(1,2)[3,8] x(2,3)[5,10]

19 Harbin Institute of Technology Algorithm overview n 1. Sort by the end times n 2. Remove tasks cover other tasks n 3. Dynamic programming Computing x(i,j), then x(1,n) is the result [3,10] x(i,j)[s,e] x(1,1)[3,7] x(2,2)[5,9] x(3,3)[12,16] x(1,2)[3,8] x(2,3)[5,10] x(1,3) = x(1,1) U x(2,3) x x(1,2) U x(3,3) x min

20 Harbin Institute of Technology Simulation n Tossim n Four cases n Tasks are from multi-applications n Each application consists of periodical tasks

21 Harbin Institute of Technology Simulation n short sampling interval lengths

22 Harbin Institute of Technology Simulation n longer sampling interval lengths

23 Harbin Institute of Technology Simulation n Different Window size

24 Harbin Institute of Technology Simulation n Data loss

25 Harbin Institute of Technology