Algorithms for covering multiple barriers.

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 case m = 1. In this paper, we propose an O (n 2 log ⁡ n log ⁡ log ⁡ n + n m 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. [ABSTRACT FROM AUTHOR]