144 research outputs found

    Barrier Coverage with Wireless Sensor Networks

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    We study the problem of barrier coverage with a wireless sensor network. Each sensor is modelled by a point in the plane and a sensing disk or coverage area centered at the sensor's position. The barriers are usually modelled as a set of line segments on the plane. The barrier coverage problem is to add new sensors or move existing sensors on the barriers such that every point on every barrier is within the coverage area of some sensors. Barrier coverage using sensors has important applications, including intruder detection or monitoring the perimeter of a region. Given a set of barriers and a set of sensors initially located at general positions in the plane, we study three problems for relocatable sensors in the centralized setting: the feasibility problem, and the problems of minimizing the maximum or the average relocation distances of sensors (MinMax and MinSum respectively) for barrier coverage. We show that the MinMax problem is strongly NP-complete when sensors have arbitrary ranges and can move to arbitrary positions on the barrier. We also study the case when sensors are restricted to use perpendicular movement to one of the barriers. We show that when the barriers are parallel, both the MinMax and MinSum problems can be solved in polynomial time. In contrast, we show that even the feasibility problem is strongly NP-complete if two perpendicular barriers are to be covered. For the barrier coverage problem in distributed settings, we give the first distributed local algorithms for fully synchronous unoriented sensors. Our algorithms achieve barrier coverage for a line segment barrier when there are enough sensors to cover the entire barrier. Our first algorithm is oblivious and terminates in n^2 time, whereas our second one uses two bits of memory at each sensor, and takes n steps, which is asymptotically optimal. However, if the sensors are semi-synchronous, and do not share the same orientation, we show that no algorithm exists that always terminates within finite time. Finally, for sensors that share the same orientation we give an algorithm that terminates within finite time, even if all sensors are fully asynchronous. Finally, we study barrier coverage with multi-round random deployment using stationary sensors. We analyze the probability of barrier coverage with uniformly dispersed sensors as a function of parameters such as length of the barrier, the width of the intruder, the sensing range of sensors, as well as the density of deployed sensors. We propose two specific deployment strategies and analyze the expected number of deployment rounds and deployed sensors for each strategy. We present a cost model for multi-round sensor deployments, and for each deployment strategy we find the optimal density of sensors to be deployed in each round that minimizes the total expected cost. Our results are validated by extensive simulations

    On the Displacement for Covering a dd-dimensional Cube with Randomly Placed Sensors

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    Consider nn sensors placed randomly and independently with the uniform distribution in a dd-dimensional unit cube (d2d\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 dd-dimensional unit cube is completely covered, i.e., every point in the dd-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:=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 dd-dimensional unit cube and a>0a > 0. The main contribution of the paper is to show the existence of a tradeoff between the dd-dimensional cube, sensing radius and aa-total movement. The main results can be summarized as follows for the case of the dd-dimensional cube. If the dd-dimensional cube sensing radius is 12n1/d\frac{1}{2n^{1/d}} and n=mdn=m^d, for some mNm\in N, then we present an algorithm that uses O(n1a2d)O\left(n^{1-\frac{a}{2d}}\right) total expected movement (see Algorithm 2 and Theorem 5). If the dd-dimensional cube sensing radius is greater than 33/d(31/d1)(31/d1)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(n1a2d(lnnn)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

    Optimal online and offline algorithms for robot-assisted restoration of barrier coverage

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    Cooperation between mobile robots and wireless sensor networks is a line of research that is currently attracting a lot of attention. In this context, we study the following problem of barrier coverage by stationary wireless sensors that are assisted by a mobile robot with the capacity to move sensors. Assume that nn sensors are initially arbitrarily distributed on a line segment barrier. Each sensor is said to cover the portion of the barrier that intersects with its sensing area. Owing to incorrect initial position, or the death of some of the sensors, the barrier is not completely covered by the sensors. We employ a mobile robot to move the sensors to final positions on the barrier such that barrier coverage is guaranteed. We seek algorithms that minimize the length of the robot's trajectory, since this allows the restoration of barrier coverage as soon as possible. We give an optimal linear-time offline algorithm that gives a minimum-length trajectory for a robot that starts at one end of the barrier and achieves the restoration of barrier coverage. We also study two different online models: one in which the online robot does not know the length of the barrier in advance, and the other in which the online robot knows the length of the barrier. For the case when the online robot does not know the length of the barrier, we prove a tight bound of 3/23/2 on the competitive ratio, and we give a tight lower bound of 5/45/4 on the competitive ratio in the other case. Thus for each case we give an optimal online algorithm.Comment: 20 page

    Weak coverage of a rectangular barrier

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    Assume n wireless mobile sensors are initially dispersed in an ad hoc manner in a rectangular region. They are required to move to final locations so that they can detect any intruder crossing the region in a direction parallel to the sides of the rectangle, and thus provide weak bar-rier coverage of the region. We study three optimization problems related to the movement of sensors to achieve weak barrier coverage: minimizing the number of sensors moved (MinNum), minimizing the average distance moved by the sensors (MinSum), and minimizing the maximum distance moved by the sensors (

    Optimal Route Planning with Mobile Nodes in Wireless Sensor Networks

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    Wireless Sensor Networks (WSN) are a collection of sensor nodes that sense their surroundings and relay their proximal information for further analysis. They utilize wireless communication technology to allow monitoring areas remotely. A major problem with WSNs is that the sensor nodes have a set sensing radius, which may not cover the entire field space. This issue would lead to an unreliable WSN that sometimes would not discover or report about events taking place in the field space. Researchers have focused on developing techniques for improving area coverage. These include allowing mobile sensor nodes to dynamically move towards coverage holes through the use of a path planning approach to solve issues such as maximizing area coverage. An approach is proposed in this thesis to maximize the area of network coverage by the WSN through a Mixed Integer Linear Programming (MILP) formulation which utilizes both static and mobile nodes. The mobile nodes are capable of travelling across the area of interest, to cover empty ‘holes’ (i.e. regions not covered by any of the static nodes) in a WSN. The goal is to find successive positions of the mobile node through the network, in order to maximize the network area coverage, or achieve a specified level of coverage while minimizing the number of iterations taken. Simulations of the formulation on small WSNs show promising results in terms of both objectives

    Temporal vertex cover with a sliding time window.

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    Modern, inherently dynamic systems are usually characterized by a network structure which is subject to discrete changes over time. Given a static underlying graph, a temporal graph can be represented via an assignment of a set of integer time-labels to every edge, indicating the discrete time steps when this edge is active. While most of the recent theoretical research on temporal graphs focused on temporal paths and other “path-related” temporal notions, only few attempts have been made to investigate “non-path” temporal problems. In this paper we introduce and study two natural temporal extensions of the classical problem VERTEX COVER. We present a thorough investigation of the computational complexity and approximability of these two temporal covering problems. We provide strong hardness results, complemented by approximation and exact algorithms. Some of our algorithms are polynomial-time, while others are asymptotically almost optimal under the Exponential Time Hypothesis (ETH) and other plausible complexity assumptions

    Solving k

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    Coverage problem is a critical issue in wireless sensor networks for security applications. The k-barrier coverage is an effective measure to ensure robustness. In this paper, we formulate the k-barrier coverage problem as a constrained optimization problem and introduce the energy constraint of sensor node to prolong the lifetime of the k-barrier coverage. A novel hybrid particle swarm optimization and gravitational search algorithm (PGSA) is proposed to solve this problem. The proposed PGSA adopts a k-barrier coverage generation strategy based on probability and integrates the exploitation ability in particle swarm optimization to update the velocity and enhance the global search capability and introduce the boundary mutation strategy of an agent to increase the population diversity and search accuracy. Extensive simulations are conducted to demonstrate the effectiveness of our proposed algorithm

    OIL SPILL MODELING FOR IMPROVED RESPONSE TO ARCTIC MARITIME SPILLS: THE PATH FORWARD

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    Maritime shipping and natural resource development in the Arctic are projected to increase as sea ice coverage decreases, resulting in a greater probability of more and larger oil spills. The increasing risk of Arctic spills emphasizes the need to identify the state-of-the-art oil trajectory and sea ice models and the potential for their integration. The Oil Spill Modeling for Improved Response to Arctic Maritime Spills: The Path Forward (AMSM) project, funded by the Arctic Domain Awareness Center (ADAC), provides a structured approach to gather expert advice to address U.S. Coast Guard (USCG) Federal On-Scene Coordinator (FOSC) core needs for decision-making. The National Oceanic & Atmospheric Administration (NOAA) Office of Response & Restoration (OR&R) provides scientific support to the USCG FOSC during oil spill response. As part of this scientific support, NOAA OR&R supplies decision support models that predict the fate (including chemical and physical weathering) and transport of spilled oil. Oil spill modeling in the Arctic faces many unique challenges including limited availability of environmental data (e.g., currents, wind, ice characteristics) at fine spatial and temporal resolution to feed models. Despite these challenges, OR&R’s modeling products must provide adequate spill trajectory predictions, so that response efforts minimize economic, cultural and environmental impacts, including those to species, habitats and food supplies. The AMSM project addressed the unique needs and challenges associated with Arctic spill response by: (1) identifying state-of-the-art oil spill and sea ice models, (2) recommending new components and algorithms for oil and ice interactions, (3) proposing methods for improving communication of model output uncertainty, and (4) developing methods for coordinating oil and ice modeling efforts
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