TY - GEN

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.

PY - 2012

Y1 - 2012

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 (2008) introduced this problem as the geometric version of the unique coverage problem, and the best approximation ratio by van Leeuwen (2009) 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 (2008) introduced this problem as the geometric version of the unique coverage problem, and the best approximation ratio by van Leeuwen (2009) 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.

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U2 - 10.1007/978-3-642-31155-0_3

DO - 10.1007/978-3-642-31155-0_3

M3 - Conference contribution

AN - SCOPUS:84863089080

SN - 9783642311543

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 24

EP - 35

BT - Algorithm Theory, SWAT 2012 - 13th Scandinavian Symposium and Workshops, Proceedings

T2 - 13th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2012

Y2 - 4 July 2012 through 6 July 2012

ER -