Local Coverage Optimization Strategy Based on Voronoi for Directional Sensor Networks^{ †}
Abstract
:1. Introduction
 We transform the network area coverage problem into cell coverage problems by exploiting the Voronoi diagram, which only needs to optimize local coverage for each cell. The proposed approach solves the problem in a decentralized way.
 By adopting a node’s moving or rotation actions, we propose three local coverage optimization algorithms to improve the cell coverage, i.e., Move Inside Cell Algorithm (MIC), Rotate Working Direction Algorithm (RWD), Rotation based on boundary (RB), respectively.
 We use extensive simulations to prove the effectiveness of our proposed algorithms in terms of the coverage ratio. Specifically, compared to the benchmark algorithm Distributed VoronoiBased SelRedeployment algorithm (DVSA) proposed in [8], our algorithm MIC shows a shorter moving distance and lower energy consumption.
2. Related Work
3. System Model and Problem Statement
3.1. DSN Sensing Model
 Euclidean distance between p and s must be smaller than sensing radius ${R}_{s}$, i.e., $d(s,p)\le {R}_{s}$:$$d(s,p)=\sqrt{{(x{x}_{s})}^{2}+{(y{y}_{s})}^{2}}\le {R}_{s}.$$
 The absolute included angle between $\overrightarrow{wd}$ and $\overrightarrow{sp}$ must be smaller then $\alpha /2$:$$\varphi =arccos\frac{\overrightarrow{wd}\xb7\overrightarrow{sp}}{\parallel sp\parallel}\le \frac{\alpha}{2}.$$
3.2. Voronoi Diagram and Some Assumptions
 All of the directional sensors are homogeneous, that is to say, every sensor has the same sensing radius ${R}_{s}$, viewing angle α, rotation ability and mobility.
 We can obtain an accurate coordinate of every sensor node by using Global Position System (GPS) or other alternative localization algorithms such as DVhop, Amorphous, etc.
 All of the sensor nodes have strong transmission ability to ensure the network connectivity and Voronoi diagram constructed successfully.
3.3. Problem Statement
 Restrict the sensor node’s moving trace in its corresponding cell.
 Get maximal coverage in each cell and minimum overlap with another cell’s sensor fan.
 Maximize the cell coverage under the constraints of minimized moving distance.
4. Theoretical Analysis and Algorithms
4.1. To Determine Whether a Sensor’s Sector Area is Wrapped in the Cell (Gets Full Coverage)
4.2. Move and Rotate inside the Cell Based on the Vertex
4.2.1. Case 1: Rotate Working Direction Algorithm (RWD)
4.2.2. Case 2: Move Inside Cell Algorithm (MIC)
Algorithm 1 Rotate Working Direction Algorithm (RWD) 

Algorithm 2 Move Inside Cell Algorithm (MIC) 

4.3. Rotation Based on Boundary (RB)
 for boundary $x=0$,$$\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\left(\right)open="\{"\; close>\begin{array}{cc}\hfill {x}_{{a}_{l}}\le {x}_{{a}_{r}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{x}_{{a}_{l}}\le 0& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{right}\\ \hfill {x}_{{a}_{l}}0\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{x}_{{a}_{r}}\ge 0& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{right}\end{array}$$$$\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\left(\right)open="\{"\; close>\begin{array}{cc}\hfill {x}_{{a}_{r}}\le {x}_{{a}_{l}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{x}_{{a}_{r}}\ge 0& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{left}\\ \hfill {x}_{{a}_{l}}\ge 0\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{x}_{{a}_{r}}0& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{left}\end{array}$$
 for boundary $x=n$,$$\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\left(\right)open="\{"\; close>\begin{array}{cc}\hfill {x}_{{a}_{l}}\le {x}_{{a}_{r}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{x}_{{a}_{l}}\le n& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{right}\\ \hfill {x}_{{a}_{l}}\ge n\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{x}_{{a}_{l}}n& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{right}\end{array}$$$$\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\left(\right)open="\{"\; close>\begin{array}{cc}\hfill {x}_{{a}_{r}}\ge {x}_{{a}_{l}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{x}_{{a}_{l}}\ge n& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{left}\\ \hfill {x}_{{a}_{l}}n\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{x}_{{a}_{r}}\le n& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{left}\end{array}$$
 for boundary $y=0,$$$\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\left(\right)open="\{"\; close>\begin{array}{cc}\hfill {y}_{{a}_{l}}\le {y}_{{a}_{r}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{y}_{{a}_{r}}\le 0& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{right}\\ \hfill {y}_{{a}_{l}}\le 0\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{y}_{{a}_{r}}0& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{right}\end{array}$$$$\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\left(\right)open="\{"\; close>\begin{array}{cc}\hfill {y}_{{a}_{r}}\le {y}_{{a}_{l}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{y}_{{a}_{l}}\le 0& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{left}\\ \hfill {y}_{{a}_{r}}\le 0\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{y}_{{a}_{l}}0& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{left}\end{array}$$
 for boundary $y=m$$$\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\left(\right)open="\{"\; close>\begin{array}{cc}\hfill {y}_{{a}_{r}}\le {y}_{{a}_{l}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{y}_{{a}_{r}}\ge m& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{right}\\ \hfill {y}_{{a}_{r}}m\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{y}_{{a}_{l}}\ge m& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{right}\end{array}$$$$\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\left(\right)open="\{"\; close>\begin{array}{cc}\hfill {y}_{{a}_{l}}\le {y}_{{a}_{r}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{y}_{{a}_{l}}\ge m& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{left}\\ \hfill {y}_{{a}_{l}}m\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{and}\phantom{\rule{3.33333pt}{0ex}}{y}_{{a}_{r}}\ge m& \mathrm{rotate}\phantom{\rule{3.33333pt}{0ex}}\mathrm{left}\end{array}$$
5. Performance Evaluation
5.1. Sensing Coverage
5.2. Comparison from Moving Distance
5.3. Coverage Ratios with Different ${R}_{s}$ and AoV
5.4. Coverage Ratio
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
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Parameters  Value 

sensing radius  ${R}_{s}$ = 6 m, 8 m, ..., 12 m 
angle of view (AoV)  AoV = ${30}^{\circ},{60}^{\circ},...,{180}^{\circ}$ 
size of monitoring area  Area = 100 m $\times 100$ m 
the number of sensors, N  N = 40, 60, 90, ..., 300 
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CCBY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Zhang, G.; You, S.; Ren, J.; Li, D.; Wang, L. Local Coverage Optimization Strategy Based on Voronoi for Directional Sensor Networks. Sensors 2016, 16, 2183. https://doi.org/10.3390/s16122183
Zhang G, You S, Ren J, Li D, Wang L. Local Coverage Optimization Strategy Based on Voronoi for Directional Sensor Networks. Sensors. 2016; 16(12):2183. https://doi.org/10.3390/s16122183
Chicago/Turabian StyleZhang, Guanglin, Shan You, Jiajie Ren, Demin Li, and Lin Wang. 2016. "Local Coverage Optimization Strategy Based on Voronoi for Directional Sensor Networks" Sensors 16, no. 12: 2183. https://doi.org/10.3390/s16122183