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A 4.31-Approximation for the Geometric Unique Coverage Problem on Unit Disks

  • Takehiro Ito
  • Shin-ichi Nakano
  • Yoshio Okamoto
  • Yota Otachi
  • Ryuhei Uehara
  • Takeaki Uno
  • Yushi Uno
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7676)

Abstract

We give an improved approximation algorithm for the unique unit-disk coverage problem: Given a set of points and a set of unit disks, both in the plane, we wish to find a subset of disks that maximizes the number of points contained in exactly one disk in the subset. Erlebach and van Leeuwen (2008) introduced this problem as the geometric version of the unique coverage problem, and gave a polynomial-time 18-approximation algorithm. In this paper, we improve this approximation ratio 18 to \(2+ 4/\sqrt{3} +\varepsilon\) ( < 4.3095 + ε) for any fixed constant ε > 0. Our algorithm runs in polynomial time which depends exponentially on 1/ε. The algorithm can be generalized to the budgeted unique unit-disk coverage problem in which each point has a profit, each disk 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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References

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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.Tohoku UniversitySendaiJapan
  2. 2.Gunma UniversityKiryuJapan
  3. 3.University of Electro-CommunicationsChofuJapan
  4. 4.Japan Advanced Institute of Science and TechnologyNomiJapan
  5. 5.National Institute of InformaticsChiyoda-kuJapan
  6. 6.Osaka Prefecture UniversityNaka-kuJapan

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