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

N1 - Funding Information:
The authors thank anonymous referees of the preliminary version and of this journal version for their helpful suggestions. This work is partially supported by Grant-in-Aid for Scientific Research (KAKENHI) including 24106004 , 24106005 , 24220003 , 24700008 , 25330003 , 26330009 , 15H00853 , 15K00009 , and by the Funding Program for World-Leading Innovative R&D on Science and Technology, Japan.
Publisher Copyright:
© 2015 Elsevier B.V.

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

UR - http://www.scopus.com/inward/record.url?scp=84947966740&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947966740&partnerID=8YFLogxK

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 -