TY - JOUR

T1 - A polynomial-time approximation scheme for the geometric unique coverage problem on unit squares

AU - Ito, Takehiro

AU - Nakano, Shin Ichi

AU - Okamoto, Yoshio

AU - Otachi, Yota

AU - Uehara, Ryuhei

AU - Uno, Takeaki

AU - Uno, Yushi

PY - 2016/1

Y1 - 2016/1

N2 - 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.

AB - 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.

KW - Dynamic programming

KW - Polynomial-time approximation scheme

KW - Shifting strategy

KW - Unique coverage problem

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U2 - 10.1016/j.comgeo.2015.10.004

DO - 10.1016/j.comgeo.2015.10.004

M3 - Article

AN - SCOPUS:84947966740

VL - 51

SP - 25

EP - 39

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

ER -