Given a set of directional visual sensors, the @math -coverage problem determines the orientation of minimal directional sensors so that each target is covered at least @math times. As the problem is NP-complete, a number of heuristics have been devised to tackle the issue. However, the existing heuristics provide imbalance coverage of the targets--some targets are covered @math times while others are left totally uncovered or singly covered. The coverage imbalance is more serious in under-provisioned networks where there do not exist enough sensors to cover all the targets @math times. Therefore, we address the problem of covering each target at least @math times in a balanced way using minimum number of sensors. We study the existing Integer Linear Programming (ILP) formulation for single coverage and extend the idea for @math -coverage. However, the extension does not balance the coverage of the targets. We further propose Integer Quadratic Programming (IQP) and Integer Non-Linear Programming (INLP) formulations that are capable of addressing the coverage balancing. As the proposed formulations are computationally expensive, we devise a faster Centralized Greedy @math -Coverage Algorithm (CGkCA) to approximate the formulations. Finally, through rigorous simulation experiments we show the efficacy of the proposed formulations and the CGkCA.
There exist quite a few works using directional sensors. Jing and Abouzeid @cite_12 formulate the coverage problem using directional sensors as Maximum Coverage using Minimum Sensors (MCMS) problem, and provide both centralized and decentralized greedy solutions. In @cite_3 , Munishwar and Abu-Ghazaleh present new algorithm which improves the greedy approaches of @cite_12 . The optimal solution to @math -coverage problem has been proved to be NP-hard by Fusco and Gupta in @cite_7 . They also modelled the sensors to have a fixed viewing angle and overlapping pans. However, all of these works overlooked the coverage imbalance issue.
@cite_3 @cite_7 @cite_12
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We study a novel “coverage by directional sensors” problem with tunable orientations on a set of discrete targets. We propose a Maximum Coverage with Minimum Sensors (MCMS) problem in which coverage in terms of the number of targets to be covered is maximized whereas the number of sensors to be activated is minimized. We present its exact Integer Linear Programming (ILP) formulation and an approximate (but computationally efficient) centralized greedy algorithm (CGA) solution. These centralized solutions are used as baselines for comparison. Then we provide a distributed greedy algorithm (DGA) solution. By incorporating a measure of the sensors residual energy into DGA, we further develop a Sensing Neighborhood Cooperative Sleeping (SNCS) protocol which performs adaptive scheduling on a larger time scale. Finally, we evaluate the properties of the proposed solutions and protocols in terms of providing coverage and maximizing network lifetime through extensive simulations. Moreover, for the case of circular coverage, we compare against the best known existing coverage algorithm. Sensor nodes may be equipped with a "directional" sensing device (such as a camera) which senses a physical phenomenon in a certain direction depending on the chosen orientation. In this article, we address the problem of selection and orientation of such directional sensors with the objective of maximizing coverage area. Prior works on sensor coverage have largely focused on coverage with sensors that are associated with a unique sensing region. In contrast, directional sensors have multiple sensing regions associated with them, and the orientation of the sensor determines the actual sensing region. Thus, the coverage problems in the context of directional sensors entails selection as well as orientation of sensors needed to activate in order to maximize ensure coverage. In this article, we address the problem of selecting a minimum number of sensors and assigning orientations such that the given area (or set of target points) is k-covered (i.e., each point is covered k times). The above problem is NP-complete, and even NP-hard to approximate. Thus, we design a simple greedy algorithm that delivers a solution that k-covers at least half of the target points using at most M log(k|C|) sensors, where |C| is the maximum number of target points covered by a sensor and M is the minimum number of sensor required to k-cover all the given points. The above result holds for almost arbitrary sensing regions. We design a distributed implementation of the above algorithm, and study its performance through simulations. In addition to the above problem, we also look at other related coverage problems in the context of directional sensors, and design similar approximation algorithms for them. We propose new algorithms to achieve k-coverage in dense sensor networks. In such networks, covering sensor locations approximates covering the whole area. However, it has been shown before that selecting the minimum set of sensors to activate from an already deployed set of sensors is NP-hard. We propose an efficient approximation algorithm which achieves a solution of size within a logarithmic factor of the optimal. We prove that our algorithm is correct and analyze its complexity. We implement our algorithm and compare it against two others in the literature. Our results show that the logarithmic factor is only a worst-case upper bound and the solution size is close to the optimal in most cases. A key feature of our algorithm is that it can be implemented in a distributed manner with local information and low message complexity. We design and implement a fully distributed version of our algorithm. Our distributed algorithm does not require that sensors know their locations. Comparison with two other distributed algorithms in the literature indicates that our algorithm: (i) converges much faster than the others, (ii) activates near-optimal number of sensors, and (iii) significantly prolongs (almost doubles) the network lifetime because it consumes much less energy than the other algorithms. One of the research issues in wireless sensor networks (WSNs) is how to efficiently deploy sensors to cover an area. In this paper, we solve the k-coverage sensor deployment problem to achieve multi-level coverage of an area I. We consider two sub-problems: k-coverage placement and distributed dispatch problems. The placement problem asks how to determine the minimum number of sensors required and their locations in I to guarantee that I is k-covered and the network is connected; the dispatch problem asks how to schedule mobile sensors to move to the designated locations according to the result computed by the placement strategy such that the energy consumption due to movement is minimized. Our solutions to the placement problem consider both the binary and probabilistic sensing models, and allow an arbitrary relationship between the communication distance and sensing distance of sensors. For the dispatch problem, we propose a competition-based and a pattern-based schemes. The former allows mobile sensors to bid for their closest locations, while the latter allows sensors to derive the target locations on their own. Our proposed schemes are efficient in terms of the number of sensors required and are distributed in nature. Simulation results are presented to verify their effectiveness.