1. SMART: A Scan-based Movement- Assisted Sensor Deployment Method in Wireless Sensor Networks Jie Wu and Shuhui Yang Department of Computer Science and Engineering Florida Atlantic University INFOCOM 2005

2. Outline Introduction Related Works Scan-based Movement-assisted Sensor Deployment Method (SMART) Extended SMART Simulation Conclusion

3. Introduction The efficiency of a sensor network depends on the deployment and coverage of the monitoring area. A good sensor deployment is still necessary to balance the workload of sensors. Two methods used to enhance the coverage after an initial random deployment  Incremental sensor deployment  Deploys additional sensors  Movement-assisted sensor deployment  Moves the existing sensors

4. Introduction The sensor deployment problem can be viewed as load balance problem  Partitioned small region  processor  Number of sensors in a region  load Two differences between deployment and load balance  Different objectives: number of moves  Different technical issues: communication hole

5. Introduction – Basic Idea 2D scan-based movement-assisted deployment  The sensor network is partitioned into a 2-D mesh of clusters  Each cluster covers a small square area.  The cluster is controlled by a clusterhead  The clusterhead knows the cluster’s position i and the number of sensors in the cluster  Each clusterhead is in charge communication and bookkeeping  Two scans,once for rows and once for columns, are used to calculate the average load and determine the overloaded and underloaded clusters.  Load is shifted from overloaded clusters to underloaded ones.

6. Introduction – Ideal Case Example Scan in rowsScan in columns Unbalanced StateBalanced State

7. Introduction Communication hole problem: the clusters with empty size can not communication with other clusters, so the scan approach can not be used.

8. Related Works (1) Load balance in multiprocessor systems [13] [14]  Diffusion: each node exchange load with all neighbors : load in node i, j : adjacent node to i : diffusion parameter  ¼ for fastest convergence [17] in 2-D mesh  Dimension Exchange: group adjacent edges to different four dimensions, two adjacent node by the edge exchange load. : exchange rate

9. Related Works (2) Movement-assisted sensor deployment  Virtual force based mobile sensor deployment algorithm (VFA) [6]  Using the potential field to calculate virtual force  Voronoi diagram based sensor deployment algorithm [5] VEC: sensors calculate the virtual force form its Voronoi neighbor VOR: sensors detect the coverage holes and move to its farthest Voronoi vertex Minimax: sensors move to target position such that whose distance to the farthest vertex is minimized

10. SMART - Clustering Clustering  cluster  Each cluster covers square  Sensing range:  Intra-transmission range:  Inter-transmission range:  Each sensor knows its cluster id i  Each clusterhead knows its load Load (number of sensors) of a cluster

11. SMART – Scan (1) Scan for 1-D array of clusters to calculate the load in the balance state  : number of sensors in cluster i  : prefix sum of the first i clusters  : total sum  : the average load (number of sensors) in a balanced state  : prefix sum of the first i clusters in balanced state  First scan calculates, second scan sends back and calculate first second Determine state of each cluster Send back

12. SMART – Scan (2) Determine the “give/take” state of each cluster   neutral state   overloaded  give state   underloaded  take state Determine the shifted number of sensors  Overloaded clusters Give right: Give left:  Underloaded clusters Take left: Take right:

13. SMART – Properties (1) Theorem 1: Any violation of the four conditions on give and take state of each cluster will increase of overall moving distance and/or total number of moves to reach a load balanced state. Proof:  Condition 1: change a cluster i from take to give, the i gives unit to j, i still have to get a compensate from k, it will increase the moving distance.  Condition 2: change a cluster i form give to take, same as condition 1.  Condition 3: cluster i mixes take-left with take-right  Condition 4: cluster i mixes give-right with give-left, similar to condition 3.

14. SMART – Properties (2) Theorem 2: When take-right (take-left) states get load from give-left (give-right) states, the overall moving distance is independent of the actual schedule. Proof: consider from give-left states. Cluster i is in take-right state and the closest give-left cluster is i’. But now the unit to i comes from not-closest cluster j’, and unit from i’ goes to j. The following figure shows the moving distance is the same.

15. SMART – 1D Load Balance algorithm Sender-Initiated Optimal Load Balance in 1-D Arrays  For each cluster i in give state, the clusterhead sends units to its right neighbor, and sends units to its left neightbor.  For each cluster j in take state, when the cluster head senses several bypassing units, it intersects as many units as possible to fill in its “holes”, Unintersected units move along the same direction.

16. SMART – Properties(3) Theorem 3: The proposed greedy schedule ensures an optimal schedule in 1-D Arrays Proof: when a unit is passed to i from right to left, it implies that subarray [i…n] is in overloaded state; similarly, when a unit is passed to j’ from left to right, the subarray [1…j’] is overloaded. Since i < j’, the array [1…n] as a whole is overloaded, which corresponds to a contradiction.

17. SMART – Extend 1D to 2D Extend 1-D scan to 2-D  Scan procedure is applied twice: rows and column  No longer optimal  Solution: the actual movement of sensors occurs after the columns scan. Only clusters in the overloaded state with respect to the global average send load. 31 35 22 44 33 33 Scan in RowsScan in Columns Moves +2 Total Moves: 4 Optimal Moves: 2

18. Extended SMART – Filling Holes Expansion for filling holes in 1-D arrays  Notations Segment S i : sequence of non-empty clusters W i : summation load of S i C i : length of S i L i : expansion level of S i, 2 Li < C i < 2 Li+1 E i : energy level of S i, E i = W i - C i  Doubling expansion for S Expansion sequence: 2 Li, 2 Li+1, 2 Li+2,….. Expansion condition: E i > 2 Li+k Example: C i of S i is 13, 2 3 (8) < 13(C i ) < 2 3+1 (16), L i = 3, expansion of the segment will be 8, 16, 32,…..

19. Extended SMART – Holes Solution Steps of communication holes solution 1. Following the positive direction, each segment performs expansion through recursive doubling until it either reaches (covers) the last cluster of the 1-D array or fails the expansion. 2. Repeat step 1. for the negative direction.

20. Extended SMART – Properties Theorem 4: in each segment S in a pre-processing scan, the total moving distance in constructing S is bounded by C 2 and the communication latency is bounded by 5C. Theorem 5: assume the average load is at least 2 for each cluster. After the first pre-processing scan, at least one postfix of the 1-D array is a segment an all holes will be filled. Theorem 6: suppose the average number of sensors in a cluster is at least 4. after column-wise smoothing, each row will have at least 2n sensors.

21. Extended SMART – Overall SMART Revised SMART  Step 1 (column-wise smoothing): Pre-processing (fill the communication holes) on column (positive direction). Then simultaneous pre-processing and scan (load balance) on column (negative direction). Then scan on column (positive).  Step 2 (row-wise pre-processing and scan): Pre-processing on row (positive). Then simultaneous pre-processing and scan on row (negative), finally scan on row (positive).  Step 3 (column-wise scan): Scan on column (negative followed by positive).

22. Simulation(1) Environment  Simulation area: 500 x 500  Cluster numbers: n x n, n = 4, 10  Sensor numbers: N = 400 ~ 1000  Initial deployment: random and normal distribution  Normal distribution parameter o: o = 1 ~ 5

23. Simulation(2) Rounds comparison of DIFF, EXCH, and SMART

24. Simulation(3) Distance comparison of DIFF, EXCH, and SMART

25. Simulation(4) Balance degree comparison of DIFF, EXCH, and SMART

26. Simulation(5) Balance degree comparison of DIFF, EXCH, and SMART by Grads

27. Simulation(6) Comparison of VOR and SMART using different o

28. Conclusion The paper have proposed a scan-based movement- assisted sensor deployment algorithm. The algorithm also considered the communication hole problem. The algorithm achieve even deployment with modest costs. Future work contains intra-cluster balancing and depth simulation on energy consumption.