The Optimal Placement of Sensors in Square Target Regions with Varying Boundary Length

AbstractThe sensors have been applied in many different environments to detect the fire or other things. An optimal placement of sensors is needed to guarantee full coverage and to reduce the financial cost. In this paper, a target region with square boundary is studied to find a suitable placement scheme. The length of the square boundary is growing from zero to infinite, while the sensors’ sensing radius is fixed. Different schemes are discussed to fit the varying target region. The layout of the sensors is substituted by the placement of the sensing circle's inscribed polygons, which are regular triangles, squares and regular hexagons. The minimum number of sensors that each scheme needs is calculated. Through the comparison and analysis, 16 cases are summarized. Each case is given an optimal placement scheme and the minimum number of sensors that should be distributed