On Minimizing the Sum of Sensor Movements for Barrier Coverage of a Line Segment

Czyzowicz, Jurek; Kranakis, Evangelos; Kriz̧anc, Danny; Lambadaris, Ioannis; Narayanan, Lata; Opatrný, Jaroslav; Stacho, Ladislav; Urrutia, Jorge; Yazdani, Maryam

doi:10.1007/978-3-642-14785-2_3

Cited by 65 publications

(87 citation statements)

References 11 publications

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“…In this paper, we study a one-dimensional barrier coverage problem where the barrier is for a (finite) line segment and the sensors are initially located on the line containing the barrier segment and allowed to move on the line. As discussed in the previous works [8,9,16] and shown in this paper, barrier coverage even for 1D domains poses some challenging algorithmic issues. Also, our 1D solutions may be used in solving more general problems.…”

Section: Introductionmentioning

confidence: 85%

“…But, if all sensors have the same range, polynomial time algorithms were possible [15,16]. Another study of the line segment barrier [9] aimed to minimize the sum of the moving distances of all sensors; this problem is NP-hard [9], but is solvable in polynomial time when all sensors have the same range [9]. In addition, Li et al [13] considers the linear coverage problem which aims to set an energy for each sensor to form a coverage such that the cost of all sensors is minimized.…”

Section: Related Workmentioning

confidence: 99%

“…For example, research efforts were made to extend the scalability of WSNs to the monitoring of international borders [10,11]. Unlike the traditional full coverage [12,18,19] which requires an entire target region to be covered by the sensors, the barrier coverage [2,3,8,9,11] only seeks to cover the perimeter of the region to ensure that any intruders are detected as they cross the region border. Since barrier coverage requires fewer sensors, it is often preferable to full coverage.…”

Section: Introductionmentioning

confidence: 99%

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

Chen

et al. 2013

Discrete Comput Geom

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In this paper, we study the problem of moving n 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(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(n 2 ) time. We present an 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) 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) time, improving the previously best O(n 2 ) time solution.

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Section: Introductionmentioning

confidence: 85%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Chen

et al. 2013

Discrete Comput Geom

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“…The goal of the former is the monitoring of an entire region [12,14,16], on the assumption that the intruder might appear at any point in the region and must be detected within a fixed time delay. In contrast to area monitoring, the focus of barrier coverage is on the boundary of a given region [2,3,7,8,13]. Assuming that an intruder cannot enter a region without crossing its boundary, monitoring the boundary of the region is sufficient to detect all intruders with possibly fewer nodes.…”

Section: Introductionmentioning

confidence: 98%

“…Finally, in ad hoc deployment using relocatable sensors, nodes are initially located at arbitrary positions. But nodes have the capability to relocate to new positions so that the entire barrier is covered [4,7,8,19]. With deterministic deployment or using mobile sensor nodes, one can possibly use fewer nodes.…”

Section: Introductionmentioning

confidence: 99%

Distributed algorithms for barrier coverage using relocatable sensors

et al. 2016

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We study the barrier coverage problem using relocatable sensor nodes. We assume each sensor can sense an intruder or event inside its sensing range. Sensors are initially located at arbitrary positions on the barrier and can move along the barrier. The goal is to find final positions for sensors so that the entire barrier is covered. In recent years, the problem has been studied extensively in the centralized setting. In this paper, we study a barrier coverage problem in the distributed and discrete setting. We assume that we have n identical sensors located at grid positions on the barrier, and that each sensor repeatedly executes a Look-Compute-Move cycle: based on what it sees in its vicinity, it makes a decision on where to move, and moves to its next position. We make two strong but realistic restrictions on the capabilities of sensors: they have a constant visibility range and can move only a constant distance in every cycle. In this model, we give the first two distributed algorithms that achieve barrier coverage for a line segment barrier when there are enough nodes in the network to cover the entire barrier. Our algorithms are An abbreviated version of this paper is published synchronous, and local in the sense that sensors make their decisions independently based only on what they see within their constant visibility range. One of our algorithms is oblivious whereas the other uses two bits of memory at each sensor to store the type of move made in the previous step. We show that our oblivious algorithm terminates within Θ(n 2 ) steps with the barrier fully covered, while the constant-memory algorithm is shown to take Θ(n) steps to terminate in the worst case. Since any algorithm in which a sensor can only move a constant distance in one step requires Ω(n) steps on some inputs, our second algorithm is asymptotically optimal.

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Linear time algorithm for computing min‐max movement of sink‐based mobile sensors for line barrier coverage

Zou

Guo

Huang

et al. 2020

Concurrency and Computation

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Witnessing broad energy‐critical applications of barrier coverage in mobile and wireless sensor networks, emerging practical applications have recently brought a new barrier coverage model which uses sink‐based mobile sensors for covering a given barrier with the aim of prolonging the lifespan of the coverage. In the model, a set of sink stations were distributed on the plane in which each sink can emit mobile sensors with an identical radius. The task is to cover a given line barrier with the emitted mobile sensors, aiming to minimize the maximum movement of the sensors so as to prolong the shortest lifespan among the sensors in coverage. In this paper, we first devise an algorithm for optimally solving the problem based on the properties of the structures called movement parity and tangent equilibrium points between the sinks. Then based on a more sophisticated geometric property of optimum solutions, we improve the runtime to a linear runtime O(k) which attains the possibly optimum runtime of the problem for k being the number of sinks. At last, numerical experiments are carried out to demonstrate the practical performance gain of our algorithms against baselines in literature.

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On Minimizing the Sum of Sensor Movements for Barrier Coverage of a Line Segment

Cited by 65 publications

References 11 publications

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

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

Distributed algorithms for barrier coverage using relocatable sensors

Linear time algorithm for computing min‐max movement of sink‐based mobile sensors for line barrier coverage

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