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Maximizing Dominance in the Plane and Its Applications

Conference paper
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Part of the Lecture Notes in Computer Science book series (LNCS, 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 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringPohang University of Science and TechnologyPohangSouth Korea
  2. 2.Department of Mathematics, IMFMUniversity of LjubljanaLjubljanaSlovenia
  3. 3.Department of Mathematics, FMFUniversity of LjubljanaLjubljanaSlovenia

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