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

doi:10.1016/j.comgeo.2015.10.004

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

INF - System Information Sciences

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	25-39
Number of pages	15
Journal	Computational Geometry: Theory and Applications
Volume	51
DOIs	https://doi.org/10.1016/j.comgeo.2015.10.004
Publication status	Published - 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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Ito, T., Nakano, S. I., Okamoto, Y., Otachi, Y., Uehara, R., Uno, T., & Uno, Y. (2016). A polynomial-time approximation scheme for the geometric unique coverage problem on unit squares. Computational Geometry: Theory and Applications, 51, 25-39. https://doi.org/10.1016/j.comgeo.2015.10.004

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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.",

keywords = "Dynamic programming, Polynomial-time approximation scheme, Shifting strategy, Unique coverage problem",

author = "Takehiro Ito and Nakano, {Shin Ichi} and Yoshio Okamoto and Yota Otachi and Ryuhei Uehara and Takeaki Uno and Yushi Uno",

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AU - Uno, Takeaki

AU - Uno, Yushi

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