1. Minimizing Energy Expense for Chain-Based Data Gathering in Wireless Sensor Networks Li-Hsing Yen Chung Hua University Taiwan EWSN 05

2. 2 Introduction Data gathering The process of collecting sensed data from every sensor to a distance BS The process of collecting sensed data from every sensor to a distance BS Power-conserving techniques Data fusion Data fusion Multi-hop transmission Multi-hop transmission PEGASIS: chain-based data gathering Data fusion & multi-hop transmission Data fusion & multi-hop transmission

3. 3 Chain Construction in PEGASIS: Greedy Appending A greedy method: append the nearest non-chain node to the end of the chain BS Starting with the furthest node

4. 4 PEGASIS: Data Gathering The leader collects all sensed data and transmit them to the BS Nodes play the role of the leader by turns BS Current leader

5. 5 Improved Chain Construction: Greedy Insertion [DWZ03] Non-chain nodes can be considered inserting into any position within the chain Greedy appendingGreedy insertion Time complexity: O( n 2 ) Time complexity: O( n 3 )

6. 6 Energy Dissipation Model When x transmits k -bit message to y, x consumes When y receives k -bit message, y consumes d(x, y): distance between x and y  : path loss exponent

7. 7 M d : Costs of Node Pairs With Direct Communications Cost of every node pair (x, y) energy consumed in delivering a k-bit message between x and y energy consumed in delivering a k-bit message between x and y If direct transmissions are used MdMd

8. 8 Optimal Chain Problem Cost of a chain = total cost of all edges in that chain Given all node-pair costs, finding an energy-optimal chain  finding a TSP tour on a complete graph  NP-hard Traveling Salesperson Problem

9. 9 Our Idea: Virtual Chain every edge of the chain may correspond to a multi-hop data propagation path rather than a direct radio transmission Cost of the chain = 18 12 8 2 4 16 a b c d Cost of the chain = 22 edge (c, d) corresponds to path c, b, d 16 2 4 8 a b c d Triangle inequality does not hold

10. 10 M p : Costs of Node Pairs Using Shortest Paths If shortest paths are used MdMd MpMp M p [b, c] corresponds to path b, a, c M p [c, d] corresponds to path c, a, b, d

11. 11 Constructing Virtual Chains M p can be obtained by running an all-pair shortest path algorithm on input M d e.g., Floyd-Warshall: O(n 3 ) time complexity e.g., Floyd-Warshall: O(n 3 ) time complexity Virtual chains can be constructed by running any chain construction algorithm on input M p Virtual chain Greedy appending or insertion MdMd MpMp Floyd-Warshall or any other O(n 3 )

12. 12 M t : Node-Pair Costs Based on MST Getting M p is somewhat time expensive An alternative MdMd MSTMinimum-cost spanning tree algorithm MtMt Traverse along the MST Virtual chainChainconstructionalgorithm O(n 2 ) M t [i, j] is the cost of the unique path from i to j in the MST O(n 2 )

13. 13 Triangle Inequality Property (TIP) of Node Cost Pairs TIP does not hold in M d M d [i, j] may be larger than M d [i, k] + M d [k, j] M d [i, j] may be larger than M d [i, k] + M d [k, j] due to non-linear signal attenuation due to non-linear signal attenuation TIP does hold in M p TIP does hold in M p due to the property of shortest paths due to the property of shortest paths TIP does hold in M t proof is in our paper proof is in our paper

14. 14 MST-Based Chain Construction Used as an approximation to TSP problem With TIP, the cost of the chain is no more than twice of the MST Without TIP  No algorithm with constant performance ratio M d, M p, or M t MST Minimum-cost spanning tree algorithm Virtual chain Traverse the tree in prefix order O(n 2 )

15. 15 All Possible Cost Matrix/Chain Construction Combinations Chain construc- tion Cost matrix Greedy appending Greedy insertion MST traverse MdMdMdMdPEGASIS Direct- insertion* Direct- MST MpMpMpMp Shortest- appending Shortest- insertion Shortest- MST MtMtMtMt MST- appending MST- insertion MST- MST + * [DWZ03] + can be further simplified (MST-reduced)

16. 16 Time Complexity of All Methods Method Cost matrix computation Chain construction Overall PEGASIS O(n 2 ) Direct-insertion [DWZ03] O(n 2 ) O(n 3 ) Direct-MST O(n 2 ) Shortest-appending O(n 3 ) O(n 2 ) O(n 3 ) Shortest-insertion Shortest-MST O(n 2 ) O(n 3 ) MST-appending O(n 2 ) MST-insertion O(n 3 ) MST-reduced O(n 2 )

17. 17 Leader Scheduling determine which node plays the role of leader in each round of data collections The goal is to maximize the number of data collection rounds leader scheduling in PEGASIS round-robin (RR) round-robin (RR) An improvement: nodes are not allowed to be leaders if their distances to neighbors are beyond some threshold An improvement: nodes are not allowed to be leaders if their distances to neighbors are beyond some threshold

18. 18 Formulating the Problem Notation e i : energy consumed by node i in transmits a k -bit message to the BS e i : energy consumed by node i in transmits a k -bit message to the BS  i,j : energy consumed by i in transmitting to j  i,j : energy consumed by i in transmitting to j e r : energy consumed by i in receiving a msg e r : energy consumed by i in receiving a msg E i : the amount of energy i initially has E i : the amount of energy i initially has x i : the number of times i has been selected to be the leader x i : the number of times i has been selected to be the leader

19. 19 Optimal Leader Scheduling Find positive integer values of x i ’s as to maximize  x i subject to A Linear Programming Problem

20. 20 MRPF: Maximum Residual Power First In each round of data collection, selects the node that has the maximum residual power to be the leader Residual power information is piggybacked with data message as a part of the aggregated data Each node compares its power level with that attached with incoming data message and sends only the larger one

21. 21 Simulation Results: Number of Rounds Before 1st Node Dies 0 2000 4000 6000 8000 10000 12000 14000 50100200 Number of nodes Rounds PEGASIS Direct-MST Others 50 x 50 network 100 x 100 network BS is located at (50, 150)

22. 22 Number of Rounds Before 1st Node Dies (Cont.) 50 x 50 network 100 x 100 network BS is located at (50, 200)

23. 23 Number of Rounds Before 1st Node Dies (Cont.) BS is located at (50, 300) 50 x 50 network 100 x 100 network

24. 24 Performance of Leader Scheduling Algorithms (50x50 Network) BS is located at (25, 150)BS is located at (25, 250)

25. 25 Variance of Residual Power When 1st Node Dies BS is located at (25, 150)BS is located at (25, 250)

26. 26 Conclusions Optimal chain problem is NP-hard MST-appending and MST-reduced both have the merits of lower time cost and better results Optimal leader scheduling is a linear programming problem MRPF performs nearly the same as the optimal scheduling