Elsevier

Theoretical Computer Science

Volume 758, 1 February 2019, Pages 61-72
Theoretical Computer Science

Algorithms for covering multiple barriers

https://doi.org/10.1016/j.tcs.2018.08.004Get rights and content
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Abstract

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(n3logn)-time algorithm was given for the case m=1. In this paper, we propose an O(n2lognloglogn+nmlogm)-time algorithm for a more general setting with any m1, 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(nlogn)-time algorithm was known for the case m=1. We present an algorithm of O(mlogm+nlogmlogn) time for any m1. These problems may have applications in mobile sensor barrier coverage in wireless sensor networks.

Keywords

Barrier coverage
Geometric coverage
Mobile sensors
Algorithms
Data structures
Computational geometry

Cited by (0)

A preliminary version of this paper appeared in the Proceedings of the 15th Algorithms and Data Structures Symposium (WADS 2017).