Efficient Placement and Dispatch of Sensors in a Wireless Sensor Network You-Chiun Wang, Chun-Chi Hu, and Yu-Chee Tseng IEEE Transactions on Mobile Computing 2008

2 Outline  Introduction  Sensor Placement  Sensor Dispatch  Simulations  Conclusions

3 Introduction  Sensor deployment is a critical issue because it affects the cost and detection capability of a wireless sensor network  A good sensor deployment should consider both coverage and connectivity Coverage Connectivity

4 Two Issues in Sensor Deployment  Sensor placement problem: Ask how to place the least number of sensors in a field to achieve desired coverage and connectivity properties.  Sensor dispatch problem: Assume that sensors are mobilized I A I Given a set of mobile sensors and an area of interest I inside the sensing field A, to choose a subset of sensors to be delegated to I with certain objective functions such that the coverage and connectivity properties can be satisfied

5 Sensor Placement Problem I

6 Sensor Dispatch Problem A I Mobile sensor

7 Sensor Dispatch Problem A I

8 A I

9 Outline  Introduction  Sensor Placement  Sensor Dispatch  Simulations  Conclusions

10 Sensor Placement Problem A  Input: sensing field A A A is modeled as an arbitrary-shaped polygon A A may contain several obstacles  Obstacles are also modeled by polygons A  Obstacles do NOT partition A  Each sensor has a sensing distance r s and communication distance r c But we do NOT restrict the relationship between r s and r c A  Our goal is to place sensors in A to ensure both sensing coverage and network connectivity using as few sensors as possible

11 Two Intuitive Placements Consider coverage first Consider connectivity first Need to add extra sensors to maintain connectivity when Need to add extra sensors to maintain coverage when

12 Proposed Placement Algorithm A  Partition the sensing field A into two types of sub- regions: Single-row regions Single-row regions  A belt-like area between obstacles whose width is NOT larger than, where r min = min(r s, r c )  We can deploy a sequence of sensors to satisfy both coverage and connectivity Multi-row regions Multi-row regions  We need multi-rows sensors to cover such areas  Note: Obstacles may exist in such regions.

13 Step 1: Partition the Sensing Field A  From the sensing field A, we identify all single-row regions A ’ s Expand the perimeters of obstacles outwardly and A ’ s boundaries inwardly by a distance of r min If the expansion overlaps with other obstacles, then we can take a projection to obtain single-row regions  The remaining regions are multi-row regions.

14 An Example of Partition Multi-row regions Single-row regions

15 Step 2: Place Sensors in a Single-row Region  Deploy sensors along the bisector of region

16 Step 3: Place Sensors in a Multi-row Region  We first consider a 2D plane without boundaries & obstacles Deploy sensors row by row A row of sensors needs to guarantee coverage and connectivity Adjacent rows need to guarantee continuous coverage  Case 1: Sensors on each row are separated by r c Adjacent rows are separated by  Case 2: Each sensor is separated by

17 Case 1:  Sensors on each row are separated by r c  Adjacent rows are separated by

18 Case 2: Each sensor is separated by

19 Refined Step 3:  For a multi-row region with boundaries and obstacles, We can place sensors one by one according to the following locations (if it is not inside an obstacle or outside the region)

20 Step 4:  Three unsolved problems Some areas near the boundaries are uncovered Need extra sensors between adjacent rows to maintain connectivity when Connectivity to neighboring regions needs to be maintained  Solutions Sequentially place sensors along the boundaries of the regions and obstacles

21 Outline  Introduction  Sensor Placement  Sensor Dispatch  Simulations  Conclusions

22 Problem Definition  We are given A A sensing field A IA An area of interest I inside A SA A set of mobile sensors S resident in A S’SI I  The sensor dispatch problem asks how to find a subset of sensors S’ in S to be moved to I such that after the deployment, I satisfies coverage and connectivity requirements and the movement cost satisfies some objective functions.

23 Two Objective Functions  Minimize the total energy consumption to move sensors : unit energy cost to move a sensor in one step d i : the distance that sensor i is to be moved  Maximize the average remaining energy of sensors in S ’ after the movement e i : initial energy of sensor i

24 Proposed Dispatch Algorithm I A B D C E  Initially, there are five mobile sensors A, B, C, D, and E

25 Proposed Dispatch Algorithm I A B D C E I  Run sensor placement algorithm on I to get the target locations L={(x 1, y 1 ), (x 2, y 2 ), (x 3, y 3 ), (x 4, y 4 )} Step1:

26 Proposed Dispatch Algorithm I A B D C E  Compute energy cost (assume =1) Step2:

27 Proposed Dispatch Algorithm  Construct the weighted complete bipartite graph G and assign weight on each edge A B C D E S L Weights of edges (assume that all sensors have the same initial energy 40 & 2nd objective function is used) ABCDE Step3:  w(si, (xj, yj)) = - c(s i, (x j, y j )), if objective function (1) is used  w(si, (xj, yj)) = e i - c(s i, (x j, y j )), if objective function (2) is used

28 An Example of Dispatch  Construct the new graph G from G by adding |S|-|L| virtual locations  Use the Hungarian method to find a maximum-weighted perfect-matching M S L ABCDE ^ Virtual location A B C D E Min. ABCDE Step4: w min ={min. weight in G}-1.

29 An Example of Dispatch S L ABCDE A B C D E  Construct the new graph G from G by adding |S|-|L| virtual locations  Use the Hungarian method to find a maximum-weighted perfect-matching M Step4:

30 An Example of Dispatch  Move sensors to the target locations If, it means that we do not have sufficient energy to move all sensors. Then the algorithm terminates. S L A B C D E I A B D C E Do not move A BD CI E Step5:

31 Find the Shortest Distance d(s i, (x j, y j ))  Find collision-free shortest path A sensor is modeled as a circle with a radius r Expand the perimeters of obstacles by the distance of r to find the collision-free vertices. Connect all pairs of vertices, as long as the corresponding edges do not cross any obstacle. Using Dijkstra ’ s algorithm to find the shortest path.

32 Time complexity  The time complexity of this sensor dispatch algorithm is O( mnk 2 )+ O( nm )+ O( n ( n - m ))+ O( n 3 ) + O( n ) = O( mnk 2 + n 3 ) I m: number of target locations in I n: number of mobile sensors I k: number of vertices of the polygons of all obstacles and I

33 A Distributed Dispatch Algorithm I A B D C E  Initially, there are five mobile sensors A, B, C, D, and E

34 A Distributed Dispatch Algorithm I A B D C E I  The sink runs the placement algorithm on I to obtain a set of locations L = {(x 1, y 1 ); … ; (x m, y m )} The sink then broadcasts L to all sensors Step1:

35 A Distributed Dispatch Algorithm I A B D C E  Compute energy cost (assume =1) Step2: A B C D E

36 A Distributed Dispatch Algorithm I A B D C E  Compute energy cost (assume =1) Step3: A B C D E

37 A Distributed Dispatch Algorithm I Step4: A D C E B ABCDE Step5: Destination Table  On s i ’ s way moving toward its destination, it will periodically broadcast the status of its table L, its destination, and its cost to move to that destination. The above action can be controlled by setting a timer T broadcast.  Each sensor will repeat the above steps until it reaches its destination or loses to another sensor and finds that all locations in L have been marked as occupied.

38 Outline  Introduction  Sensor Placement  Sensor Dispatch  Simulations  Conclusions

39 Simulations  Sensing fields

40 Simulation Parameters  (r s, r c ) = (7,5), (5,5), (3.5,5), (2,5) to reflect the four cases  Comparison metric Average number of sensors used to deploy Compare with two deployment methods Coverage-firstConnectivity-first

41 Simulations (r s vs. r c )

42 Simulations Parameters - Dispatch Algorithm  The sensing field A is a 900m x 900m square.  The region of interest I is a 300m x 300m square located at the center of A.  Sensors are randomly scattered over the region of A.  The setting of (r c, r s ) = (28, 16), (23.5, 13.45), (21, 12), (19.5,11.05), (17.5, 10.1), (16.5, 9.45), and (15.5, 8.9) we will need 150, 200, 250, 300, 350, 400, and 450 sensors

43 Simulations - Dispatch Algorithm

44 Simulations - Dispatch Algorithm

45 Simulations - Distributed Dispatch Algorithm (a) The number of sensor is 200

46 Simulations - Distributed Dispatch Algorithm (b) The number of sensor is 400

47 Conclusions  This paper propose a systematical solution for sensor deployment Sensing field is modeled as an arbitrary polygon with obstacles Allow arbitrary relationship between r c and r s Fewer sensors are required to ensure coverage and connectivity  A new sensor dispatch problem is defined and two energy-efficient dispatch algorithms are presented

Thanks~~

49 Proposed Dispatch Algorithm (I) I  Step1: Run any sensor placement algorithm on I to get the target locations L={(x 1, y 1 ), …,(x m, y m )}  Step2: For each sensor, determine the energy cost c(s i, (x j, y j )) to move s i to each location (x j, y j ))  Step3: Construct a weighted complete bipartite graph, such that the weight of each edge is w(s i, (x j, y j )) = - c(s i, (x j, y j )), if objective function (1) is used w(s i, (x j, y j )) = e i - c(s i, (x j, y j )), if objective function (2) is used

50 Proposed Dispatch Algorithm (II)  Step4: Construct a new graph from G, where L is a set of |S|-|L| elements, each called a virtual location. The weights of edges incident to L are set to w min, where w min ={min. weight in G}-1.  Find the maximum-weight perfect-matching M on graph G by using the Hungarian method.  Step5: For each edge c(s i, (x j, y j )) in M such that, move sensor s i to location (x j, y j ) via the shortest path. If, it means that we do not have sufficient energy to move all sensors. Then the algorithm terminates. ^ ^ ^ ^^^ ^

51 Find the Maximum-Weight Perfect-Matching

52 The Hungarian Method

53 A Distributed Dispatch Algorithm I  Step1: The sink runs the placement algorithm on the area I to obtain a set of locations L = {(x 1, y 1 ); … ; (x m, y m )} to be occupied by sensors. The sink then broadcasts L to all sensors.  Step2: On receiving the table L, a sensor will keep a copy of L and mark each location (x j, y j ) as unoccupied.  Step3: Each sensor s i then chooses an unoccupied location (x j ; y j ) from L as its destination. The selection of (x j ; y j ) is dependent on our objective function.

54 A Distributed Dispatch Algorithm  Step4: On s i ’ s way moving toward its destination, it will periodically broadcast the status of its table L, its destination, and its cost to move to that destination. The above action can be controlled by setting a timer T broadcast. For all locations marked as occupied by s i, s k will also mark them as occupied. If both s i and s k are moving toward the same destination, they will compete by their costs.  The one with a lower cost will win and keep moving toward that destination.  The one with a higher cost will give up moving toward that destination and go back to step 3 to reselect a new destination.

55 A Distributed Dispatch Algorithm  Step5: Each sensor will repeat the above steps until it reaches its destination or loses to another sensor and finds that all locations in L have been marked as occupied.