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International Symposium on Algorithms and Computation

ISAAC 2015: Algorithms and Computation pp 188–198Cite as

Minimizing the Maximum Moving Cost of Interval Coverage

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9472))

Abstract

In this paper, we study an interval coverage problem. We are given n intervals of the same length on a line L and a line segment B on L. Each interval has a nonnegative weight. The goal is to move the intervals along L such that every point of B 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 \(O(n^2\log n\log \log n)\) time. The problem has applications in mobile sensor barrier coverage.

H. Wang was supported in part by NSF under Grant CCF-1317143. Part of the work by X. Zhang was carried out during his visit at Utah State University.

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Notes

  1. 1.

    It might be more natural to pick the rightmost sensor of \(S_{i1}\) as \(s_{g(i)}\). In fact, an arbitrary one is sufficient.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Utah State University, Logan, UT, 84322, USA

    Haitao Wang

  2. Department of Computer Science, City University of Hong Kong, Kowloon Tong, Hong Kong

    Xiao Zhang

Authors
  1. Haitao Wang
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  2. Xiao Zhang
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Correspondence to Haitao Wang .

Editor information

Editors and Affiliations

  1. Masdar Institute, Abu Dhabi, United Arab Emirates

    Khaled Elbassioni

  2. Kyoto University, Kyoto, Japan

    Kazuhisa Makino

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Wang, H., Zhang, X. (2015). Minimizing the Maximum Moving Cost of Interval Coverage. In: Elbassioni, K., Makino, K. (eds) Algorithms and Computation. ISAAC 2015. Lecture Notes in Computer Science(), vol 9472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48971-0_17

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  • DOI: https://doi.org/10.1007/978-3-662-48971-0_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48970-3

  • Online ISBN: 978-3-662-48971-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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