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 (

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

Investigations on two classes of covering problems

Covering problems fall within the broader category of facility location, a branch of combinatorial optimization concerned with the optimal placement of service facilities in some geometric space. This thesis considers two classes of covering problems. The first, Covering with Variable Capacities (CVC), was introduced in [1] and adds a notion of capacity to the classical Uncapacitated Facility Location problem. That is, each facility has a fixed maximum quantity of clients it can serve. The objective of each variant of CVC is either to serve all clients, the greatest number of clients possible, or all clients using the least number of facilities possible. We provide approximation algorithms, and in a few select cases, optimal algorithms, for all three variants of CVC. The second class of covering problems is barrier coverage. When the purpose of coverage is surveillance rather than service, a cost effective approach to the problem of intruder detection is to place sensors along the boundary, or barrier, of the surveilled region. A barrier coverage is complete when any intrusion is sure to be detected by some sensor. We limit our consideration of barrier coverage to the one-dimensional case, where the region is a line segment. Sensors are themselves line segments, whose span forms a detection range. The objective of barrier coverage as considered here is to form a complete barrier coverage while minimizing the total movement cost, the sum of the weighted distances moved by each sensor in the solution. We show that, by assuming the sensors lie in initial positions where their detection ranges are disjoint from the barrier, one-dimensional barrier coverage can be solved with an FPTAS. Along the way to developing the FPTAS, we give a fast, simple 2-approximation algorithm for weighted disjoint barrier coverage

Complexity of barrier coverage with relocatable sensors in the plane

We consider several variations of the problems of covering a set of barriers (modeled as line segments) using sensors that can detect any intruder crossing any of the barriers. Sensors are initially located in the plane and they can relocate to the barriers. We assume that each sensor can detect any intruder in a circular area centered at the sensor. Given a set of barriers and a set of sensors located in the plane, we study three problems: the feasibility of barrier coverage, the problem of minimizing the largest relocation distance of a sensor (MinMax), and the problem of minimizing the sum of relocation distances of sensors (MinSum). When sensors are permitted to move to arbitrary positions on the barrier, the problems are shown to be NP-complete. We also study the case when sensors use perpendicular movem

Complexity of barrier coverage with relocatable sensors in the plane

We consider several variations of the problems of covering a set of barriers (modeled as line segments) using sensors that can detect any intruder crossing any of the barriers. Sensors are initially located in the plane and they can relocate to the barriers. We assume that each sensor can detect any intruder in a circular area of fixed range centered at the sensor. Given a set of barriers and a set of sensors located in the plane, we study three problems: (i) the feasibility of barrier coverage, (ii) the problem of minimizing the largest relocation distance of a sensor (MinMax), and (iii) the problem of minimizing the sum of relocation distances of sensors (MinSum). When sensors are permitted to move to arbitrary positions on the barrier, the MinMax problem is shown to be strongly NP-complete for sensors with arbitrary ranges. 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, even if the sensors are located at integer positions, and have only two possible sensing ranges. On the other hand, we give an O(n3/2) algorithm for a natural special case of this last problem