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. 2017 Oct 10;17(10):2304.
doi: 10.3390/s17102304.

On Efficient Deployment of Wireless Sensors for Coverage and Connectivity in Constrained 3D Space

Chase Q Wu  1 , Li Wang  2
Affiliations

On Efficient Deployment of Wireless Sensors for Coverage and Connectivity in Constrained 3D Space

Chase Q Wu et al. Sensors (Basel). .

Abstract

Sensor networks have been used in a rapidly increasing number of applications in many fields. This work generalizes a sensor deployment problem to place a minimum set of wireless sensors at candidate locations in constrained 3D space to k-cover a given set of target objects. By exhausting the combinations of discreteness/continuousness constraints on either sensor locations or target objects, we formulate four classes of sensor deployment problems in 3D space: deploy sensors at Discrete/Continuous Locations (D/CL) to cover Discrete/Continuous Targets (D/CT). We begin with the design of an approximate algorithm for DLDT and then reduce DLCT, CLDT, and CLCT to DLDT by discretizing continuous sensor locations or target objects into a set of divisions without sacrificing sensing precision. Furthermore, we consider a connected version of each problem where the deployed sensors must form a connected network, and design an approximation algorithm to minimize the number of deployed sensors with connectivity guarantee. For performance comparison, we design and implement an optimal solution and a genetic algorithm (GA)-based approach. Extensive simulation results show that the proposed deployment algorithms consistently outperform the GA-based heuristic and achieve a close-to-optimal performance in small-scale problem instances and a significantly superior overall performance than the theoretical upper bound.

Keywords: approximation algorithm; k-coverage; network connectivity; sensor deployment.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Illustration of two intersection cases between a new circle and the existing circles: (a) the new circle c′ intersects only one arc of an existing circle; (b) the new circle c′ intersects two arcs of an existing circle.
Figure 2
Figure 2
An example of Algorithm 2.
Figure 3
Figure 3
Intersected circles and divisions.
Figure 4
Figure 4
A tight example of Theorem 6.
Figure 5
Figure 5
Comparison of the average performance with the standard deviation between GreedyDLDT (Greedy), Genetic Algorithm (GA), and Optimal Algorithm (OPT) for DLDT in response to a varying number of target points.
Figure 6
Figure 6
Measured average approximation ratio of GreedyDLDT for DLDT in response to a varying number of target points.
Figure 7
Figure 7
Comparison of the average performance with the standard deviation between GreedyDLDT (Greedy), Genetic Algorithm (GA), and Optimal Algorithm (OPT) for DLDT in response to varying k values.
Figure 8
Figure 8
Measured average approximation ratio of GreedyDLDT for DLDT in response to varying k values.
Figure 9
Figure 9
Performance comparison of GreedyDLDT (Greedy), Genetic Algorithm (GA), and Optimal Algorithm (OPT) for a museum exhibition hall with sensor mounting constraints in response to a varying number of exhibition items.
Figure 10
Figure 10
Comparison of the average performance with the standard deviation between the 2-stage Greedy Algorithm, Genetic Algorithm (GA), and the Optimal Algorithm (OPT) for C-DLDT in response to a varying number of target points.
Figure 11
Figure 11
Comparison of the average performance with the standard deviation between the 2-stage Greedy Algorithm, Genetic Algorithm (GA), and the Optimal Algorithm (OPT) for C-DLDT in response to varying k values.
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