Efficient Placement and Dispatch of Sensors in a

Efficient Placement and Dispatch of Sensors in a Wireless Sensor Network Prof. Yu-Chee Tseng Department of Computer Science National Chiao-Tung University 1

Outline o o Introduction Sensor Placement Sensor Dispatch Conclusions 2

Introduction o Wireless sensor networks (WSN) n n n o Tiny, low-power devices Sensing units, transceiver, actuators, and even mobilizers Gather and process environmental information WSN applications n n n Surveillance Biological detection Monitoring 3

Introduction o o 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

Review o o The art gallery problem (AGP) asks how to use a minimum set of guards in a polygon such that every point of the polygon is watched by at least one guard. However, the results cannot be directly applied to sensor deployment problem because n AGP typically assumes that a guard can watch a point as long as line-of-sight exists o n Sensing distance of a sensor is normally finite AGP does NOT address the communication issue between guards o Sensor deployment needs to address the connectivity issue 5

Two Issues in Sensor Deployment o Sensor placement problem: n o Ask how to place the least number of sensors in a field to achieve desired coverage and connectivity properties. Sensor dispatch problem: n Assume that sensors are mobilized n 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 6

Outline o o Introduction Sensor Placement Sensor Dispatch Conclusions 7

Sensor Placement Problem o Input: sensing field A n n A is modeled as an arbitrary-shaped polygon A may contain several obstacles o o o Each sensor has a sensing distance rs and communication distance rc n o Obstacles are also modeled by polygons Obstacles do NOT partition A But we do NOT restrict the relationship between rs and rc Our goal is to place sensors in A to ensure both sensing coverage and network connectivity using as few sensors as possible 8

Two Intuitive Placements Consider coverage first Need to add extra sensors to maintain connectivity when Consider connectivity first Need to add extra sensors to maintain coverage when 9

Proposed Placement Algorithm o Partition the sensing field A into two types of subregions: n Single-row regions o o n A belt-like area between obstacles whose width is NOT larger than , where rmin= min(rs, rc) We can deploy a sequence of sensors to satisfy both coverage and connectivity Multi-row regions o o We need multi-rows sensors to cover such areas Note: Obstacles may exist in such regions. 10

Step 1: Partition the Sensing Field o o From the sensing field A, we identify all single-row regions n Expand the perimeters of obstacles outwardly and A’s boundaries inwardly by a distance of rmin n 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. 11

An Example of Partition Si gio e r w ro ngle- Mul ti-ro w re ns gion s 12

Step 2: Place Sensors in a Single-row Region o Deploy sensors along the bisector of region 13

Step 3: Place Sensors in a Multi-row Region o We first consider a 2 D plane without boundaries & obstacles n n n o Case 1: n n o Deploy sensors row by row A row of sensors needs to guarantee coverage and connectivity Adjacent rows need to guarantee continuous coverage Sensors on each row are separated by rc Adjacent rows are separated by Case 2: n Each sensor is separated by 14

Case 1: 15

Case 2: 16

Refined Step 3: o For a multi-row region with boundaries and obstacles, n We can place sensors one by one according to the following locations (if it is not inside an obstacle or outside the region) 17

Step 4: o Three unsolved problems n n n o 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 n Sequentially place sensors along the boundaries of the regions and obstacles 18

Simulation Results o Sensing fields 19

Simulation Parameters o o We use (rs, rc) = (7, 5), (5, 5), (3. 5, 5), (2, 5) to reflect the four cases Comparison metric n n Average number of sensors used to deploy Compare with two deployment methods Coverage-first Connectivity-first 20

Simulations (rs vs. rc) 21

Simulations (Shapes of A) 22

Outline o o Introduction Sensor Placement Sensor Dispatch Conclusions 23

Problem Definition o o We are given n A sensing field A n An area of interest I inside A n A set of mobile sensors S resident in A 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. 24

Example A I Mobile sensor 25

Example A I 26

Example A I 27

Two Objective Functions o Minimize the total energy consumption to move sensors n n o : unit energy cost to move a sensor in one step di : the distance that sensor i is to be moved Maximize the average remaining energy of sensors in S’ after the movement n ei : initial energy of sensor i 28

Proposed Dispatch Algorithm (I) o o Run any sensor placement algorithm on I to get the target locations L={(x 1, y 1), … , (xm, ym)} For each sensor , determine the energy cost c(si, (xj, yj)) to move si to each location (xj, yj)) n o Construct a weighted complete bipartite graph , such that the weight of each edge is n n w(si, (xj, yj)) = - c(si, (xj, yj)) , if objective function (1) is used; or as w(si, (xj, yj)) = ei - c(si, (xj, yj)), if objective function (2) is used 29

Proposed Dispatch Algorithm (II) o o o ^ ^ Construct a new graph ^ from ^ L is a set of |S|-|L| elements, each called a G, where virtual location. The weights of edges incident to L^ are set to wmin, where wmin ={min. weight in G}-1. Find the maximum-weight perfect-matching M on graph G^ by using the Hungarian method. ^, For each edge c(si, (xj, yj)) in M such that move sensor si to location (xj, yj) via the shortest path. n If , it means that we do not have sufficient energy to move all sensors. Then the algorithm terminates. 30

An Example of Dispatch I o C Initially, there are five mobile sensors A, B, C, D, and E A B E D 31

An Example of Dispatch I A 1 2 3 4 B E o C 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)} D 32

An Example of Dispatch I A 1 2 3 4 B E o Compute energy cost (assume =1) C D 33

An Example of Dispatch Construct the weighted complete bipartite graph G and assign weight on each o edge A 1 B 2 C 3 D 4 E S L Weights of edges (assume that all sensors have the same initial energy 40 & 1 st objective function is used) 1 2 3 4 A 31 28 32 29 B 29 29 31 31 C 30 36 29 32 D 26 27 38 30 E 7 5 10 9 34

An Example of Dispatch Construct the new graph G^ from G by adding |S|-|L| virtual locations o Weights of edges A 1 B 2 C 3 D 4 E 5 S L 1 2 3 4 5 A 31 28 32 29 4 Virtual location B 29 29 31 31 4 C 30 34 29 32 4 D 26 27 28 30 4 E 7 5 10 9 4 Min. 35

An Example of Dispatch Use the Hungarian method to find a maximum-weighted perfect-matching M o Weights of edges A 1 B 2 C 3 D 4 E 5 S L 1 2 3 4 5 A 31 28 32 29 4 B 29 29 31 31 4 C 30 34 29 32 4 D 26 27 28 30 4 E 7 5 10 9 4 36

An Example of Dispatch I A A 1 C 2 3 B 4 D B E Do not move o C D Move sensors to the target locations A 1 B 2 C 3 D 4 E 5 S L 37

Find the Shortest Distance d(si, (xj, yj)) o Find collision-free shortest path n n 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. 38

Find the Maximum-Weight Perfect-Matching 39

The Hungarian Method 40

Time complexity o The time complexity of our sensor dispatch algorithm is O(mnk 2 + n 3) n m: number of target locations in I n n n: number of mobile sensors k: number of vertices of the polygons of all obstacles and I 41

Simulations o o Greedy: sensors select the closest locations Random: sensors randomly select locations 42

Conclusions o We propose a systematical solution for sensor deployment n n Sensing field is modeled as an arbitrary polygon with obstacles Allow arbitrary relationship between rc and rs Fewer sensors are required to ensure coverage and connectivity An optimal-energy dispatch algorithm is presented to move sensors to the target locations under two energybased objective functions 43