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Mrinal Nandi, Coverage problem in two and three dimension, Eur. J. Math. Appl. 3 (2023), Article ID 11.

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Volume 3 (2023), Article ID 11

https://doi.org/10.28919/ejma.2023.3.11

Published: 25/07/2023

Abstract:

Coverage in wireless sensor networks (WSNs) is a well known problem. Here we consider that problem in continuous domain. In this paper, we discuss coverage criteria and placement of sensors optimally in $\mathbb{R}^2$ and $\mathbb{R}^3$. Coverage is important in WSNs. WSNs may be two and three dimensional in real life. In practice, sensors usually dropped randomly from space on previously determined positions (called, vertices) of the ROI (Region of Interest). But sensors will not place on the proper vertices in many times. Hence ROI will not be totally covered by the deployed sensors. The question is, how we reduced the area which is not covered by sensors? Usually extra sensors are dropped on some randomly but previously chosen points to minimize the uncovered area. In the current paper, we develop another strategy for deployment of those sensors. We partition the ROI in regular hexagons in two dimension and face-centered cubes in three dimension. Our new strategy is to reduce the side of hexagons or cubes. The amount of reduction depends on the number of extra sensors used. Here we target to deploy exactly one sensor randomly on each vertices. We compare uncovered volume for the two strategies, for two distributions (uniform and normal), and several number of excess sensors used. Simulation result shows that our new strategy is better for lower variance of the randomness but old one is better for higher variance.

How to Cite:

Mrinal Nandi, Coverage problem in two and three dimension, Eur. J. Math. Appl. 3 (2023), Article ID 11. https://doi.org/10.28919/ejma.2023.3.11