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

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

Barrier Coverage with Wireless Sensor Networks

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

Weak coverage of a rectangular barrier

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 (

Algorithms for Covering Barrier Points by Mobile Sensors with Line Constraint

In this thesis, we develop efficient algorithms for the problem of covering barrier points by mobile sensors. Each sensor is represented by a point in the plane with the same covering range r so that any point within distance r from the sensor can be covered by the sensor. Given a set B of m points (called “barrier points”) and a set S of n points (representing the “sensors”) in the plane, the problem is to move the sensors so that each barrier point is covered by at least one sensor and the maximum movement of all sensors is minimized. The problem is NP-hard. In this thesis, we consider two line-constrained variations of the problem and present efficient algorithms that improve the previous work. In the first problem, all sensors are given on a line l and are required to move on l only while the barrier points can be anywhere in the plane. We propose an O((n+m) log(n+m)) time algorithm for the problem. We also consider the weighted case where each sensor has a weight; we give an O((m+n) log2(m+n)) time algorithm for this case. In the second problem, all barrier points are on l while all sensors are in the plane but are required to move to l to cover all barrier points. We solve the weighted case in O(mlogm+nlog2n) time

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

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

Solving k

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