Barrier Coverage in Wireless Sensor Networks

Barrier coverage is a critical issue in wireless sensor networks (WSNs) for security applications, which aims to detect intruders attempting to penetrate protected areas. However, it is difficult to achieve desired barrier coverage after initial random deployment of sensors because their locations cannot be controlled or predicted. In this dissertation, we explore how to leverage the mobility capacity of mobile sensors to improve the quality of barrier coverage. We first study the 1-barrier coverage formation problem in heterogeneous sensor networks and explore how to efficiently use different types of mobile sensors to form a barrier with pre-deployed different types of stationary sensors. We introduce a novel directional barrier graph model and prove that the minimum cost of mobile sensors required to form a barrier with stationary sensors is the length of the shortest path from the source node to the destination node on the graph. In addition, we formulate the problem of minimizing the cost of moving mobile sensors to fill in the gaps on the shortest path as a minimum cost bipartite assignment problem and solve it in polynomial time using the Hungarian algorithm. We further study the k-barrier coverage formation problem in sensor networks. We introduce a novel weighted barrier graph model and prove that determining the minimum number of mobile sensors required to form k-barrier coverage is related with but not equal to finding k vertex-disjoint paths with the minimum total length on the WBG. With this observation, we propose an optimal algorithm and a faster greedy algorithm to find the minimum number of mobile sensors required to form k-barrier coverage. Finally, we study the barrier coverage formation problem when sensors have location errors. We derive the minimum number of mobile sensors needed to fill in a gap with a guarantee when location errors exist and propose a progressive method for mobile sensor deployment. Furthermore, we propose a fault tolerant weighted barrier graph to find the minimum number of mobile sensors needed to form barrier coverage with a guarantee. Both analytical and experimental studies demonstrated the effectiveness of our proposed algorithms

Barrier Coverage with Non-uniform Lengths to Minimize Aggregate Movements

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

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 (

Snowboard, Ski, and Skateboard Sensor System Application

The goal of this project was develop a sensor for the commercial market for skiers, snowboarders, and skateboarders that can give them the data such as speed, elevation, pressure, temperature, flex, acceleration, position, and other performance data such as trick characterization. This was done by using a variety of sensors, including a GPS, flex sensors, accelerometer, and others to provide data such as speed, position, position, and temperature. The sensors were placed in an external polycarbonate casing attached to the ski or board by using an adhesive pad on the bottom of the casing. These sensors then transmit the data via a microcontroller to either an LCD screen displaying a simple application or a memory system. The user can then access and analyze this data using Matlab code to interpret its relevancy. Using this system, performance data was recorded to analyze tricks such as spins and jumps

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