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On Minimizing the Sum of Sensor Movements for Barrier Coverage of a Line Segment
"... Abstract. A set of sensors establishes barrier coverage of a given line segment if every point of the segment is within the sensing range of a sensor. Given a line segment I, n mobile sensors in arbitrary initial positions on the line (not necessarily inside I) and the sensing ranges of the sensors, ..."
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Abstract. A set of sensors establishes barrier coverage of a given line segment if every point of the segment is within the sensing range of a sensor. Given a line segment I, n mobile sensors in arbitrary initial positions on the line (not necessarily inside I) and the sensing ranges of the sensors, we are interested in finding final positions of sensors which establish a barrier coverage of I so that the sum of the distances traveled by all sensors from initial to final positions is minimized. It is shown that the problem is NP complete even to approximate up to constant factor when the sensors may have different sensing ranges. When the sensors have an identical sensing range we give several efficient algorithms to calculate the final destinations so that the sensors either establish a barrier coverage or maximize the coverage of the segment if complete coverage is not feasible while at the same time the sum of the distances traveled by all sensors is minimized. Some open problems are also mentioned. Key words and phrases: Mobile Sensor, Barrier Coverage, Line segment,
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 solv ..."
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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(n2 logn log log n) time algorithm. For the special case when all sensors have the samesize sensing range, the previously best solution takes O(n2) 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 samesize sensing range, we solve the cycle version in O(n) time. 1
Maximizing barrier coverage lifetime with mobile sensors
 In Proceedings of Algorithms – ESA ’13, LNCS v. 8125
, 2013
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On Routing, Backbone Formation and Barrier Coverage in Wireless Ad Hoc and Sensor Networks
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Complexity of barrier coverage with relocatable sensors in the plane
 In Proceedings of CIAC 2013 conference, LNCS v. 7878
, 2013
"... We consider several variations of the problems of covering a set of barriers using sensors so that sensors 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 c ..."
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We consider several variations of the problems of covering a set of barriers using sensors so that sensors 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 NPhard. We also study the case when sensors use perpendicular movement to one of the barriers, thereby moving to the closest point on the barrier. 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 NPcomplete if two perpendicular barriers are to be covered, even if the sensors are located at integer positions, and have only two possible sizes. On the other hand, we give an O(n3/2) algorithm for the case when the sensors form a nonoverlapping arrangement. 1
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 an ..."
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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 NPcomplete 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
Optimization Problems in Infrastructure Security
"... Abstract. How do we identify and prioritize risks and make smart choices based on fiscal constraints and limited resources? The main goal of infrastructure security is to secure, withstand, and rapidly recover from potential threats that may affect critical resources located within a given bounded r ..."
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Abstract. How do we identify and prioritize risks and make smart choices based on fiscal constraints and limited resources? The main goal of infrastructure security is to secure, withstand, and rapidly recover from potential threats that may affect critical resources located within a given bounded region. In order to strengthen and maintain secure, functioning, and resilient critical infrastructure, proactive and coordinated efforts are necessary. Motivated from questions raised by infrastructure security, in this paper we survey several recent optimization problems whose solution has occupied (and continues to occupy) computer science researchers in the last few years. Topics discussed include:
Barrier Coverage by Sensors with Adjustable Ranges
"... One of the most fundamental tasks of wireless sensor networks is to provide coverage of the deployment region. We study the coverage of a line interval with a set of wireless sensors with adjustable coverage ranges. Each coverage range of a sensor is an interval centered at that sensor whose length ..."
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One of the most fundamental tasks of wireless sensor networks is to provide coverage of the deployment region. We study the coverage of a line interval with a set of wireless sensors with adjustable coverage ranges. Each coverage range of a sensor is an interval centered at that sensor whose length is decided by the power the sensor chooses. The objective is to find a range assignment with the minimum cost. There are two variants of the optimization problem. In the discrete variant, each sensor can only choose from a finite set of powers, whereas in the continuous variant, each sensor can choose power from a given interval. For the discrete variant of the problem, a polynomialtime exact algorithm is designed. For the continuous variant of the problem, NPhardness of the problem is proved and followed by an ILP formulation. Then, constantapproximation algorithms are designed when the cost for all sensors is proportional to rκ for some constant κ ≥ 1, where r is the covering radius corresponding to the chosen power. Specifically, if κ = 1, we give a 1.25approximation algorithm and a fully polynomialtime approximation scheme; if κ> 1, we give a 2approximation algorithm. We also show that the approximation analyses are tight.
Applied Probability Trust (10 November 2015) SENSOR ALLOCATION PROBLEMS ON THE REAL LINE
"... A large number n of sensors (finite connected intervals) are placed randomly on the real line so that the distances between the consecutive midpoints are independent random variables with expectation inversely proportional to n. In this work we address two fundamental sensor allocation problems. Int ..."
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A large number n of sensors (finite connected intervals) are placed randomly on the real line so that the distances between the consecutive midpoints are independent random variables with expectation inversely proportional to n. In this work we address two fundamental sensor allocation problems. Interference problem tries to reallocate the sensors from their initial positions so as to eliminate overlaps. Coverage problem, on the other hand, allows overlaps, but tries to eliminate uncovered spaces between the originally placed sensors. Both problems seek to minimize the total sensor movement while reaching their respective goals. Using tools from queueing theory, Skorokhod reflections and weak convergence, we investigate the asymptotic behaviour of the optimal costs as n increases to infinity. The introduced methodology is then used to address a more complicated, modified coverage problem, in which the overlaps between any two sensors can not exceed a certain parameter.
An Optimal Algorithm for Coverage Hole Healing in Hybrid Sensor Networks
"... Abstract—Network coverage is one of the most decisive factors for determining the efficiency of a wireless sensor network. However, in dangerous or hostile environments such as battle fields or active volcano areas, we can neither deterministically or purposely deploy sensors as desired, thus the em ..."
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Abstract—Network coverage is one of the most decisive factors for determining the efficiency of a wireless sensor network. However, in dangerous or hostile environments such as battle fields or active volcano areas, we can neither deterministically or purposely deploy sensors as desired, thus the emergence of coverage holes (the unmonitored areas) is unavoidable. In addition, the introduction of new coverage holes during network operation due to sensor failures due to energy depletion shall significantly reduce coverage efficacy. Therefore, we need to either remotely control or set up a protocol to heal them as soon as possible in an automated fashion. In this paper, we focus on how to schedule mobile sensors in order to cope with coverage hole issues in a hybrid sensor network containing both static and mobile sensors. To this end, we introduce a new metric, namely to maximize the minimum remaining energy of all moved sensor since the more energy remains, the longer the network can operate. Based on this metric, we propose an efficient coverage healing algorithm that always determines an optimal location for each mobile sensor in order to heal all coverage holes, after all mobile sensors locations and coverage holes are located. Simulation results confirm the efficiency and utilization of our proposed method. Index Terms—hybrid sensor network; coverage hole, movement schedule, mobile sensor, coverage hole healing I.