Movement-efficient Sensor Deployment in Wireless Sensor Networks

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

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

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.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 With Limited Communication Range.

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 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

A study of sensor movement and selection strategies for strong barrier coverage

Intruder detection and border surveillance are some of the many applications of sensor networks. In these applications, sensors are deployed along the perimeter of a protected area such that no intruder can cross the perimeter without being detected. The arrangement of sensors for this purpose is referred to as the barrier coverage problem in sensor networks. A primary question centering such a problem is: How to achieve barrier coverage? On the other hand, sensor nodes are usually battery-powered and have limited energy. It is critical to design energy-efficient barrier construction schemes while satisfying the coverage requirement. First, we studied how to achieve strong barrier coverage with mobile sensors. We leverage the mobility of sensors and relocate them to designated destinations to form a strong horizontal barrier after the random deployment. Algorithms were proposed to calculate the optimal relocating destinations such that the maximum moving distance of sensors is minimized. Depending on the number of sensors on the final barrier, two problems were investigated: (1) constructing a barrier with the minimum number of sensors on the final barrier, and (2) constructing a barrier with any number of sensors on the final barrier. For both problems, we optimized the barrier location instead of fixing it a priori as other works. We proposed algorithms which first identify a set of discrete candidates for the barrier location, then check the candidates iteratively. Both problems could be solved in polynomial time. Second, we investigated how to achieve strong barrier coverage by selectively activating randomly deployed static sensors. We aimed to select the minimum number of sensors to be active to achieve barrier coverage under a practical probabilistic model. The system false alarm probability and detection probability were jointly considered, and a (P_D^{min}, P_F^{max})-barrier coverage was defined where P_D^{min} is the minimum system detection probability and P_F^{max} is the maximum system false alarm probability. Our analysis showed that with the constraint on the system false alarm probability, the number of active sensors affects the detection capability of sensors, which would bring new challenges to the min-num sensor selection problem. We proposed an iterative framework to solve the sensor selection problem under the probabilistic model. Depending on whether the decision fusion was applied, different detection capability evaluation methods were used in the iterative framework. Finally, we studied how to achieve strong barrier coverage in a hybrid network with a mix of mobile and static sensors. A two-step deployment strategy was adopted where static sensors are first randomly deployed, and then mobile sensors are deployed to merge the coverage gap left by the static sensors. We aimed to find the proper coverage gaps to deploy mobile sensors such that (P_D^{min}, P_F^{max})-barrier coverage is achieved, and the total cost of the barrier is minimized. Under the probabilistic model, we solved the problem by iteratively trying multiple assumptions of the number of active sensors, and obtained the min-cost deployment strategy with the help of graph algorithms

Maximizing Barrier Coverage Lifetime with Mobile Sensors

Sensor networks are ubiquitously used for detection and tracking and as a result covering is one of the main tasks of such networks. We study the problem of maximizing the coverage lifetime of a barrier by mobile sensors with limited battery powers, where the coverage lifetime is the time until there is a breakdown in coverage due to the death of a sensor. Sensors are first deployed and then coverage commences. Energy is consumed in proportion to the distance traveled for mobility, while for coverage, energy is consumed in direct proportion to the radius of the sensor raised to a constant exponent. We study two variants which are distinguished by whether the sensing radii are given as part of the input or can be optimized, the fixed radii problem and the variable radii problem. We design parametric search algorithms for both problems for the case where the final order of the sensors is predetermined and for the case where sensors are initially located at barrier endpoints. In contrast, we show that the variable radii problem is strongly NP-hard and provide hardness of approximation results for fixed radii for the case where all the sensors are initially co-located at an internal point of the barrier

Geometric Algorithms for Intervals and Related Problems

In this dissertation, we study several problems related to intervals and develop efficient algorithms for them. Interval problems have many applications in reality because many objects, values, and ranges are intervals in nature, such as time intervals, distances, line segments, probabilities, etc. Problems on intervals are gaining attention also because intervals are among the most basic geometric objects, and for the same reason, computational geometry techniques find useful for attacking these problems. Specifically, the problems we study in this dissertation includes the following: balanced splitting on weighted intervals, minimizing the movements of spreading points, dispersing points on intervals, multiple barrier coverage, and separating overlapped intervals on a line. We develop efficient algorithms for these problems and our results are either first known solutions or improve the previous work. In the problem of balanced splitting on weighted intervals, we are given a set of n intervals with non-negative weights on a line and an integer k ≥ 1. The goal is to find k points to partition the line into k + 1 segments, such that the maximum sum of the interval weights in these segments is minimized. We give an algorithm that solves the problem in O(n log n) time. Our second problem is on minimizing the movements of spreading points. In this problem, we are given a set of points on a line and we want to spread the points on the line so that the minimum pairwise distance of all points is no smaller than a given value δ. The objective is to minimize the maximum moving distance of all points. We solve the problem in O(n) time. We also solve the cycle version of the problem in linear time. For the third problem, we are given a set of n non-overlapping intervals on a line and we want to place a point on each interval so that the minimum pairwise distance of all points are maximized. We present an O(n) time algorithm for the problem. We also solve its cycle version in O(n) time. The fourth problem is on multiple barrier coverage, where we are given n sensors in the plane and m barriers (represented by intervals) on a line. The goal is to move the sensors onto the line to cover all the barriers such that the maximum moving distance of all sensors is minimized. Our algorithm for the problem runs in O(n2 log n log log n + nm log m) time. In a special case where the sensors are all initially on the line, our algorithm runs in O((n + m) log(n + m)) time. Finally, for the problem of separating overlapped intervals, we have a set of n intervals (possibly overlapped) on a line and we want to move them along the line so that no two intervals properly intersect. The objective is to minimize the maximum moving distance of all intervals. We propose an O(n log n) time algorithm for the problem. The algorithms and techniques developed in this dissertation are quite basic and fundamental, so they might be useful for solving other related problems on intervals as well