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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)


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.


  • 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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Correspondence to Hee-Kap Ahn .

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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.

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  • Print ISBN: 978-3-030-24765-2

  • Online ISBN: 978-3-030-24766-9

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