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Max-Min Dispersion on a Line

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Combinatorial Optimization and Applications (COCOA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11346))

Abstract

Given a set P of n locations on which facilities can be placed and an integer k, we want to place k facilities on some locations so that a designated objective function is maximized. The problem is called the k-dispersion problem.

In this paper we give a simple O(n) time algorithm to solve the max-min version of the k-dispersion problem if P is a set of points on a line. This is the first O(n) time algorithm to solve the max-min k-dispersion problem for the set of “unsorted” points on a line.

If P is a set of sorted points on a line, and the input is given as an array in which the coordinates of the points are stored in the sorted order, then by slightly modifying the algorithm above one can solve the dispersion problem in \(O(\log n)\) time. This is the first sublinear time algorithm to solve the max-min k-dispersion problem for the set of sorted points on a line.

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Author information

Authors and Affiliations

  1. Tokyo Metropolitan University, Hachioji, Japan

    Tetsuya Araki

  2. Gunma University, Kiryu, Japan

    Shin-ichi Nakano

Authors
  1. Tetsuya Araki
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  2. Shin-ichi Nakano
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Corresponding author

Correspondence to Shin-ichi Nakano .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Kennesaw State University, Marietta, GA, USA

    Donghyun Kim

  2. Department of Mathematics and Computer Science, North Carolina Central University, Durham, NC, USA

    R. N. Uma

  3. Department of Computer Science, Georgia State University, Atlanta, GA, USA

    Alexander Zelikovsky

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Araki, T., Nakano, Si. (2018). Max-Min Dispersion on a Line. In: Kim, D., Uma, R., Zelikovsky, A. (eds) Combinatorial Optimization and Applications. COCOA 2018. Lecture Notes in Computer Science(), vol 11346. Springer, Cham. https://doi.org/10.1007/978-3-030-04651-4_45

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  • DOI: https://doi.org/10.1007/978-3-030-04651-4_45

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04650-7

  • Online ISBN: 978-3-030-04651-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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