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Workshop on Algorithms and Data Structures

WADS 2019: Algorithms and Data Structures pp 325–338Cite as

Maximizing Dominance in the Plane and Its Applications

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11646)

Abstract

Given a set P of n points with weights (possibly negative), a set Q of m points in the plane, and a positive integer k, we consider the optimization problem of finding a subset of Q with at most k points that dominates a subset of P with maximum total weight. We say a set of points \(Q'\) dominates p if some point q of \(Q'\) satisfies \(x(p)\leqslant x(q)\) and \(y(p)\leqslant y(q)\). We present an efficient algorithm solving this problem in \(O(k(n+m)\log m)\) time and \(O(n+m)\) space. Our result implies algorithms with better time bounds for related problems, including the disjoint union of cliques problem for interval graphs (equivalently, the hitting intervals problem) and the top-k representative skyline points problem in the plane.

Keywords

  • Dominance
  • Disjoint cliques
  • Hitting intervals

Work by Choi and Ahn was supported by the MSIT (Ministry of Science and ICT), Korea, under the SW Starlab support program (IITP-2017-0-00905) supervised by the IITP (Institute of Information & communications Technology Planning & Evaluation.). Work by Cabello was supported by the Slovenian Research Agency, program P1-0297 and projects J1-8130, J1-8155, J1-9109.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Pohang University of Science and Technology, Pohang, South Korea

    Jongmin Choi & Hee-Kap Ahn

  2. Department of Mathematics, IMFM, University of Ljubljana, Ljubljana, Slovenia

    Sergio Cabello

  3. Department of Mathematics, FMF, University of Ljubljana, Ljubljana, Slovenia

    Sergio Cabello

Authors
  1. Jongmin Choi
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  2. Sergio Cabello
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  3. Hee-Kap Ahn
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Corresponding author

Correspondence to Hee-Kap Ahn .

Editor information

Editors and Affiliations

  1. Department of Computing Science, University of Alberta, Edmonton, AB, Canada

    Dr. Zachary Friggstad

  2. School of Computer Science, Carleton University, Manotick, ON, Canada

    Dr. Jörg-Rüdiger Sack

  3. Department of Computing Science, University of Alberta, Edmonton, AB, Canada

    Mohammad R Salavatipour

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Choi, J., Cabello, S., Ahn, HK. (2019). Maximizing Dominance in the Plane and Its Applications. In: Friggstad, Z., Sack, JR., Salavatipour, M. (eds) Algorithms and Data Structures. WADS 2019. Lecture Notes in Computer Science(), vol 11646. Springer, Cham. https://doi.org/10.1007/978-3-030-24766-9_24

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  • DOI: https://doi.org/10.1007/978-3-030-24766-9_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24765-2

  • Online ISBN: 978-3-030-24766-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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