Changing of the guards: Strip cover with duty cycling

Bar-Noy, Amotz; Baumer, Benjamin S.; Rawitz, Dror

doi:10.1016/j.tcs.2014.09.002

Cited by 6 publications

(7 citation statements)

References 15 publications

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“…Another model which can be considered is the duty cycling model in which sensors are partitioned into shifts that cover the barrier. Bar-Noy et al [3] considered this model for stationary sensors and α = 1. Extending it to moving sensors and α > 1 is an interesting research direction.…”

Section: Discussion and Open Problemsmentioning

confidence: 99%

“…The first result is obtained using a reduction from Partition. 3 Roughly speaking, our reduction uses a sensor that cannot move if it is required to maintain its radius for one unit of time. This sensor splits the line into two segments, and therefore the question of whether the given numbers can be partitioned into two subsets of equal sum translates into the question of whether we can cover the two segments for some time interval.…”

Section: C1 Fixed Radiimentioning

confidence: 99%

“…Buchsbaum et al [6] and Gibson and Varadarajan [11] considered the Restricted Strip Covering in which sensors are static and radii are fixed, but sensors may start covering at any time. Bar Noy et al [2,3,4] considered the variant of this problem in which the radii are adjustable.…”

Section: Introductionmentioning

confidence: 99%

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Maximizing Barrier Coverage Lifetime with Mobile Sensors

Bar-Noy¹,

Rawitz²,

Terlecky³

2017

SIAM J. Discrete Math.

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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.

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Section: Discussion and Open Problemsmentioning

confidence: 99%

Section: C1 Fixed Radiimentioning

confidence: 99%

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Maximizing Barrier Coverage Lifetime with Mobile Sensors

Bar-Noy¹,

Rawitz²,

Terlecky³

2017

SIAM J. Discrete Math.

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“…• Decrease the battery and the radius of the left-most sensor as much as possible, and also decrease the battery and the radius of the right-most sensor as much as possible. ), (3,4) , while at the bottom, I ′ j = ( Observation 4. Let sensors 1 and m be the leftmost and rightmost sensors in x j .…”

Section: Cutting the Schedule Into Stripsmentioning

confidence: 99%

“…Motivated by prior invocations of duty cycling [19,17,1,7,9,10], Bar-Noy et al [4] studied a duty cycle variant of OnceSC with unit batteries in which sensors must be grouped into shifts of size at most k that take turns covering [0,1]. (RoundRobin is the only possible algorithm when k = 1.)…”

Section: Introductionmentioning

confidence: 99%

Set It and Forget It: Approximating the Set Once Strip Cover Problem

2016

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We consider the Set Once Strip Cover problem, in which n wireless sensors are deployed over a one-dimensional region. Each sensor has a fixed battery that drains in inverse proportion to a radius that can be set just once, but activated at any time. The problem is to find an assignment of radii and activation times that maximizes the length of time during which the entire region is covered. We show that this problem is NP-hard. Second, we show that RoundRobin, the algorithm in which the sensors take turns covering the entire region, has a tight approximation guarantee of 3 2 in both Set Once Strip Cover and the more general Strip Cover problem, in which each radius may be set finitely-many times. Moreover, we show that the more general class of duty cycle algorithms, in which groups of sensors take turns covering the entire region, can do no better. Finally, we give an optimal O(n 2 log n)-time algorithm for the related Set Radius Strip Cover problem, in which sensors must be activated immediately.

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“Green” Barrier Coverage with Mobile Sensors

Bar-Noy

Rawitz

Terlecky

2015

Lecture Notes in Computer Science

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Mobile sensors are located on a barrier represented by a line segment. Each sensor has a single energy source that can be used for both moving and sensing. A sensor consumes energy in movement in proportion to distance traveled, and it expends energy per time unit for sensing in direct proportion to its radius raised to a constant exponent. We address the problem of energy efficient coverage. The input consists of the initial locations of the sensors and a coverage time requirement t. A feasible solution consists of an assignment of destinations and coverage radii to all sensors such that the barrier is covered. We consider two variants of the problem that are distinguished by whether the radii are given as part of the input. In the fixed radii case, we are also given a radii vector ρ, and the radii assignment r must satisfy r i ∈ {0, ρ i }, for every i, while in the variable radii case the radii assignment is unrestricted. The goal is to cover the barrier for t time in an energy efficient manner. More specifically, we consider two objective functions. In the first the goal is to minimize the sum of the energy spent by all sensors and in the second the goal is to minimize the maximum energy used by any sensor.We present fully polynomial time approximation schemes for the problem of minimizing the energy sum with variable radii and for the problem of minimizing the maximum energy with variable radii. We also show that the latter can be approximated within any additive constant ε > 0. We present a 2-approximation algorithm for the problem of minimizing the maximum energy with fixed radii which also is shown to be strongly NP-hard. We show that the problem of minimizing the energy sum with fixed radii cannot be approximated within a factor of O(n c ), for any constant c, unless P=NP. Additional results are given for three special cases: (i) sensors are stationary, (ii) free movement, and (iii) uniform fixed radii.

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Changing of the guards: Strip cover with duty cycling

Cited by 6 publications

References 15 publications

Maximizing Barrier Coverage Lifetime with Mobile Sensors

Maximizing Barrier Coverage Lifetime with Mobile Sensors

Set It and Forget It: Approximating the Set Once Strip Cover Problem

“Green” Barrier Coverage with Mobile Sensors

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