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

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 [9] introduced this problem as the geometric version of the unique coverage problem, and the best approximation ratio by van Leeuwen [21] 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.

Original languageEnglish
Pages (from-to)25-39
Number of pages15
JournalComputational Geometry: Theory and Applications
Volume51
DOIs
Publication statusPublished - 2016 Jan

Keywords

  • Dynamic programming
  • Polynomial-time approximation scheme
  • Shifting strategy
  • Unique coverage problem

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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