A Polynomial-Time Approximation Scheme for the Geometric Unique Coverage Problem on Unit Squares

  • Takehiro Ito
  • Shin-Ichi Nakano
  • Yoshio Okamoto
  • Yota Otachi
  • Ryuhei Uehara
  • Takeaki Uno
  • Yushi Uno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7357)

Abstract

We give a polynomial-time approximation scheme for the unique unit-square coverage problem: given a set of points and a set of axis-parallel unit squares, both in the plane, we wish to find a subset of squares that maximizes the number of points contained in exactly one square in the subset. Erlebach and van Leeuwen (2008) introduced this problem as the geometric version of the unique coverage problem, and the best approximation ratio by van Leeuwen (2009) before our work was 2. Our scheme can be generalized to the budgeted unique unit-square coverage problem, in which each point has a profit, each square has a cost, and we wish to maximize the total profit of the uniquely covered points under the condition that the total cost is at most a given bound.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Takehiro Ito
    • 1
  • Shin-Ichi Nakano
    • 2
  • Yoshio Okamoto
    • 3
  • Yota Otachi
    • 4
  • Ryuhei Uehara
    • 4
  • Takeaki Uno
    • 5
  • Yushi Uno
    • 6
  1. 1.Graduate School of Information SciencesTohoku UniversityJapan
  2. 2.Department of Computer ScienceGunma UniversityJapan
  3. 3.Department of Communication Engineering and InformaticsUniversity of Electro-CommunicationsJapan
  4. 4.School of Information ScienceJAISTJapan
  5. 5.Principles of Informatics Research DivisionNational Institute of InformaticsJapan
  6. 6.Graduate School of ScienceOsaka Prefecture UniversityJapan

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