Minimizing the Aggregate Movements for Interval Coverage

Andrews, A. M.; Wang, Haitao

doi:10.1007/s00453-016-0153-8

Cited by 23 publications

(17 citation statements)

References 18 publications

(28 reference statements)

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“…The non-uniform case of the problem is NP-hard [8]. For the uniform case, Czyzowicz et al [8] gave an O(n 2 ) time algorithm, and recently, Andrews and Wang [1] proposed an O(n log n) time solution. Another variation of the problem is the min-num version, where the goal is to move the minimum number of sensors to form a barrier coverage.…”

Section: Related Workmentioning

confidence: 99%

“…We "parameterize" our decision algorithm with λ as a parameter. Although we do not know the value λ * , we execute the decision algorithm in such a way that it will determine the same solution subset of sensors s g (1) , s g (2) , . .…”

Section: An Overviewmentioning

confidence: 99%

“…Let Λ denote the set of all event values. In addition, we add λ 1 i−1 and λ 2 i−1 to Λ. Next we sort all values in Λ.…”

mentioning

confidence: 99%

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Minimizing the Maximum Moving Cost of Interval Coverage

Lee

Wang

Zhang

2017

Int. J. Comput. Geom. Appl.

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In this paper, we consider an interval coverage problem. We are given [Formula: see text] intervals of the same length on a line [Formula: see text] and a line segment [Formula: see text] on [Formula: see text]. Each interval has a nonnegative weight. The goal is to move the intervals along [Formula: see text] such that every point of [Formula: see text] is covered by at least one interval and the maximum moving cost of all intervals is minimized, where the moving cost of each interval is its moving distance times its weight. Algorithms for the “unweighted” version of this problem have been given before. In this paper, we present a first-known algorithm for this weighted version and our algorithm runs in [Formula: see text] time. The problem has applications in mobile sensor barrier coverage, where [Formula: see text] is the barrier and each interval is the covering interval of a mobile sensor.

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Section: Related Workmentioning

confidence: 99%

Section: An Overviewmentioning

confidence: 99%

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Minimizing the Maximum Moving Cost of Interval Coverage

Lee

Wang

Zhang

2017

Int. J. Comput. Geom. Appl.

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“…For the same setting, the case of heterogeneous sensors was shown to be also solvable in polynomial time in [7], and the algorithm of [8] for the homogeneous case was also improved. An O(n 2 ) algorithm for the MinSum problem with homogeneous sensors is given in [9], and an improved O(n log n) algorithm is presented in [1]. It was proved in [9] that the MinSum problem is NP-hard when sensors have heterogeneous ranges.…”

Section: Related Workmentioning

confidence: 99%

Weak Coverage of a Rectangular Barrier

Dobrev

Kranakis

Kriz̧anc

et al. 2017

Lecture Notes in Computer Science

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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 barrier 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 (MinMax). We give an O(n 3/2 ) time algorithm for the MinNum problem for sensors of diameter 1 that are initially placed at integer positions; in contrast we show that the problem is NP-hard even for sensors of diameter 2 that are initially placed at integer positions. We show that the MinSum problem is solvable in O(n log n) time for homogeneous range sensors in arbitrary initial positions for the Manhattan metric, while it is NP-hard for heterogeneous sensor ranges for both Euclidean and Manhattan metrics. Finally, we prove that even very restricted homogeneous versions of the MinMax problem are NP-hard.

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“…If sensors have different ranges, then the problem is NP-hard [8]. Otherwise, Czyzowicz et al [8] gave an O(n 2 ) time algorithm, and Andrews and Wang [1] improved the algorithm to O(n log n) time. The min-num version of the problem was also studied, where the goal is to move the minimum number of sensors to form a barrier coverage.…”

Section: Related Workmentioning

confidence: 99%

Algorithms for Covering Multiple Barriers

Wang

2017

Lecture Notes in Computer Science

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In this paper, we consider the problems for covering multiple intervals on a line. Given a set B of m line segments (called "barriers") on a horizontal line L and another set S of n horizontal line segments of the same length in the plane, we want to move all segments of S to L so that their union covers all barriers and the maximum movement of all segments of S is minimized. Previously, an O(n 3 log n)-time algorithm was given for the case m = 1. In this paper, we propose an O(n 2 log n log log n + nm log m)-time algorithm for a more general setting with any m ≥ 1, which also improves the previous work when m = 1. We then consider a line-constrained version of the problem in which the segments of S are all initially on the line L. Previously, an O(n log n)-time algorithm was known for the case m = 1. We present an algorithm of O(m log m + n log m log n) time for any m ≥ 1. These problems may have applications in mobile sensor barrier coverage in wireless sensor networks.

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Minimizing the Aggregate Movements for Interval Coverage

Cited by 23 publications

References 18 publications

Minimizing the Maximum Moving Cost of Interval Coverage

Minimizing the Maximum Moving Cost of Interval Coverage

Weak Coverage of a Rectangular Barrier

Algorithms for Covering Multiple Barriers

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