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Algorithms for Covering Multiple Barriers

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)

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 \(O(n^3\log n)\)-time algorithm was given for the problem but only for the special case \(m=1\). In this paper, we propose an \(O(n^2\log n\log \log n+nm\log m)\)-time algorithm for any m, which improves the previous work even for \(m=1\). 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 \(O((n+m)\log (n+ m))\) time for any m. These problems may have applications in mobile sensor barrier coverage in wireless sensor networks.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceUtah State UniversityLoganUSA

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