8,269 research outputs found

    On the Displacement for Covering a dβˆ’d-dimensional Cube with Randomly Placed Sensors

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    Consider nn sensors placed randomly and independently with the uniform distribution in a dβˆ’d-dimensional unit cube (dβ‰₯2d\ge 2). The sensors have identical sensing range equal to rr, for some r>0r >0. We are interested in moving the sensors from their initial positions to new positions so as to ensure that the dβˆ’d-dimensional unit cube is completely covered, i.e., every point in the dβˆ’d-dimensional cube is within the range of a sensor. If the ii-th sensor is displaced a distance did_i, what is a displacement of minimum cost? As cost measure for the displacement of the team of sensors we consider the aa-total movement defined as the sum Ma:=βˆ‘i=1ndiaM_a:= \sum_{i=1}^n d_i^a, for some constant a>0a>0. We assume that rr and nn are chosen so as to allow full coverage of the dβˆ’d-dimensional unit cube and a>0a > 0. The main contribution of the paper is to show the existence of a tradeoff between the dβˆ’d-dimensional cube, sensing radius and aa-total movement. The main results can be summarized as follows for the case of the dβˆ’d-dimensional cube. If the dβˆ’d-dimensional cube sensing radius is 12n1/d\frac{1}{2n^{1/d}} and n=mdn=m^d, for some m∈Nm\in N, then we present an algorithm that uses O(n1βˆ’a2d)O\left(n^{1-\frac{a}{2d}}\right) total expected movement (see Algorithm 2 and Theorem 5). If the dβˆ’d-dimensional cube sensing radius is greater than 33/d(31/dβˆ’1)(31/dβˆ’1)12n1/d\frac{3^{3/d}}{(3^{1/d}-1)(3^{1/d}-1)}\frac{1}{2n^{1/d}} and nn is a natural number then the total expected movement is O(n1βˆ’a2d(ln⁑nn)a2d)O\left(n^{1-\frac{a}{2d}}\left(\frac{\ln n}{n}\right)^{\frac{a}{2d}}\right) (see Algorithm 3 and Theorem 7). In addition, we simulate Algorithm 2 and discuss the results of our simulations

    Movement-Efficient Sensor Deployment in Wireless Sensor Networks With Limited Communication Range.

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    We study a mobile wireless sensor network (MWSN) consisting of multiple mobile sensors or robots. Three key factors in MWSNs, sensing quality, energy consumption, and connectivity, have attracted plenty of attention, but the interaction of these factors is not well studied. To take all the three factors into consideration, we model the sensor deployment problem as a constrained source coding problem. %, which can be applied to different coverage tasks, such as area coverage, target coverage, and barrier coverage. Our goal is to find an optimal sensor deployment (or relocation) to optimize the sensing quality with a limited communication range and a specific network lifetime constraint. We derive necessary conditions for the optimal sensor deployment in both homogeneous and heterogeneous MWSNs. According to our derivation, some sensors are idle in the optimal deployment of heterogeneous MWSNs. Using these necessary conditions, we design both centralized and distributed algorithms to provide a flexible and explicit trade-off between sensing uncertainty and network lifetime. The proposed algorithms are successfully extended to more applications, such as area coverage and target coverage, via properly selected density functions. Simulation results show that our algorithms outperform the existing relocation algorithms

    Algorithms on Minimizing the Maximum Sensor Movement for Barrier Coverage of a Linear Domain

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    In this paper, we study the problem of moving nn sensors on a line to form a barrier coverage of a specified segment of the line such that the maximum moving distance of the sensors is minimized. Previously, it was an open question whether this problem on sensors with arbitrary sensing ranges is solvable in polynomial time. We settle this open question positively by giving an O(n2log⁑n)O(n^2 \log n) time algorithm. For the special case when all sensors have the same-size sensing range, the previously best solution takes O(n2)O(n^2) time. We present an O(nlog⁑n)O(n \log n) time algorithm for this case; further, if all sensors are initially located on the coverage segment, our algorithm takes O(n)O(n) time. Also, we extend our techniques to the cycle version of the problem where the barrier coverage is for a simple cycle and the sensors are allowed to move only along the cycle. For sensors with the same-size sensing range, we solve the cycle version in O(n)O(n) time, improving the previously best O(n2)O(n^2) time solution.Comment: This version corrected an error in the proof of Lemma 2 in the previous version and the version published in DCG 2013. Lemma 2 is for proving the correctness of an algorithm (see the footnote of Page 9 for why the previous proof is incorrect). Everything else of the paper does not change. All algorithms in the paper are exactly the same as before and their time complexities do not change eithe

    Movement-efficient Sensor Deployment in Wireless Sensor Networks

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    We study a mobile wireless sensor network (MWSN) consisting of multiple mobile sensors or robots. Two key issues in MWSNs - energy consumption, which is dominated by sensor movement, and sensing coverage - have attracted plenty of attention, but the interaction of these issues is not well studied. To take both sensing coverage and movement energy consumption into consideration, we model the sensor deployment problem as a constrained source coding problem. %, which can be applied to different coverage tasks, such as area coverage, target coverage, and barrier coverage. Our goal is to find an optimal sensor deployment to maximize the sensing coverage with specific energy constraints. We derive necessary conditions to the optimal sensor deployment with (i) total energy constraint and (ii) network lifetime constraint. Using these necessary conditions, we design Lloyd-like algorithms to provide a trade-off between sensing coverage and energy consumption. Simulation results show that our algorithms outperform the existing relocation algorithms.Comment: 18 pages, 10 figure

    Barrier Coverage with Non-uniform Lengths to Minimize Aggregate Movements

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    Given a line segment I=[0,L], the so-called barrier, and a set of n sensors with varying ranges positioned on the line containing I, the barrier coverage problem is to move the sensors so that they cover I, while minimising the total movement. In the case when all the sensors have the same radius the problem can be solved in O(n log n) time (Andrews and Wang, Algorithmica 2017). If the sensors have different radii the problem is known to be NP-hard to approximate within a constant factor (Czyzowicz et al., ADHOC-NOW 2009). We strengthen this result and prove that no polynomial time rho^{1-epsilon}-approximation algorithm exists unless P=NP, where rho is the ratio between the largest radius and the smallest radius. Even when we restrict the number of sensors that are allowed to move by a parameter k, the problem turns out to be W[1]-hard. On the positive side we show that a ((2+epsilon)rho+2/epsilon)-approximation can be computed in O(n^3/epsilon^2) time and we prove fixed-parameter tractability when parameterized by the total movement assuming all numbers in the input are integers
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