A Near-Optimal Sensor Placement Algorithm to Achieve Complete Coverage/Discrimination in Sensor Networks Authors : Frank Y. S. Lin and P. L. Chiu, Student Member, IEEE Presenter : Mun Chang-min Korea University of Technology and Education department of electrical & electronic engineering UoC lab heroant@kut.ac.kr

distributed sensor networks (DSNs) ◊ random placement(deployment) - when the environment is unknown, random placement is the only choice. ◊ with grid-based placement - to guarantee a particular quality of service, if the properties of the terrain are predetermined. The field is generally divided into grids and sensors are carefully deployed at the grid points.

Grid-based placement ◊ It can be represented as a collection of two- or three-dimensional grid points Grid point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Grid-based placement ◊ A set of sensors can be deployed on the grid points to monitor the sensor field. Grid point Sensors coverage 1 2 3 4 5 Sensor 6 7 8 9 10 11 12 13 14 15

Completely discriminated field ◊ Power vector - is defined for each grid point to indicate whether sensors can cover a grid point in a sensor field. ex) power vector of grid point 8 = (0, 0, 1, 1, 0, 0) corresponding to sensor 4, 6, 7, 9, 10 and 12 ◊ Completely discriminated sensor field - each grid point is identified by a unique power vector.

Not completely discriminated field ◊ Indistinguishable grid points - but, the field is completely covered. power vector of grid point 1 ║ power vector of grid point 2 1 7 6 2

Optimal Sensor Placement ◊ If complete discrimination is not possible, High discrimination requires that the maximum distance error be minimized. ◊ In this case, optimal sensor placement problem, therefore, defined as a min-max model.

Min max model ◊ Given Parameters: - A = {1, 2, ...,m} : Index set of the sensors’ candidate locations. - B = {1, 2, ..., n} : Index set of the locations in the sensor field, m ≤ n - rk : Detection radius of the sensor located at k, k ∈ A. - dij : Euclidean distance between location I and j, i, j ∈ B. - ck : The cost of the sensor allocated at location k, k ∈ A. - G : Total cost limitation. ◊ Decision Variables: - yk : 1, if a sensor is allocated at location - k and 0 otherwise, k ∈ A. - vi = (vi1, vi2, ..., vik) : The power vector of location I, where vik is 1 if the target at location i can be detected by the sensor at location k and 0 otherwise, where i ∈ B, k ∈ A.

Min max model

Proposed algorithm

Eaxperiment 1 K = 10000 ∀Ci = 1, (1 ≤ i ≤ n) ◊ Find a minimum sensor density for a complete covered and discriminated (Parameters of the cooling schedule) α = 0.75 β = 1.3 R = 5n t = 0.1 n = amount of grids tf = t0 / 30 K = 10000 ∀Ci = 1, (1 ≤ i ≤ n) Exhaustive search Proposed algorithm 65minutes 0.1second To find the solution for the 10x3 area

Experiment 2 ◊ Larger sensor fields, with 10x10 and 30x30 grid points, are considered. ◊ Find a minimum sensor density for a complete covered and discriminated compared with random placement approach.

Experiment 2 25% 44% Completely discriminated Completely covered 25% 44% Completely discriminated 42% 54% Completely covered 24% 63% 44% 69%

Thank you for listening conclusions ◊ the proposed algorithm is very effective, scalable, and robust. Thank you for listening