TY - JOUR

T1 - A 4.31-approximation for the geometric unique coverage problem on unit disks

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 ( 21700009 , 22310089 , 23500005 , 23500013 , 23500022 , 24106005 , 24220003 , 24700008 , 25106504 , 25106508 , 25330003 , 25730003 ), and by the Funding Program for World-Leading Innovative R&D on Science and Technology, Japan ( JST PRESTO, Developing Algorithmic Paradigm for Similarity Structure Analysis in Large Scale Data).

PY - 2014

Y1 - 2014

N2 - We give an improved approximation algorithm for the unique unit-disk coverage problem: Given a set of points and a set of unit disks, both in the plane, we wish to find a subset of disks that maximizes the number of points contained in exactly one disk in the subset. Erlebach and van Leeuwen (2008) introduced this problem as the geometric version of the unique coverage problem, and gave a polynomial-time 18-approximation algorithm. In this paper, we improve this approximation ratio 18 to 2+4/√3+ε (<. 4.3095. +. ε) for any fixed constant ε. >. 0. Our algorithm runs in polynomial time which depends exponentially on 1/ε. The algorithm can be generalized to the budgeted unique unit-disk coverage problem in which each point has a profit, each disk 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 an improved approximation algorithm for the unique unit-disk coverage problem: Given a set of points and a set of unit disks, both in the plane, we wish to find a subset of disks that maximizes the number of points contained in exactly one disk in the subset. Erlebach and van Leeuwen (2008) introduced this problem as the geometric version of the unique coverage problem, and gave a polynomial-time 18-approximation algorithm. In this paper, we improve this approximation ratio 18 to 2+4/√3+ε (<. 4.3095. +. ε) for any fixed constant ε. >. 0. Our algorithm runs in polynomial time which depends exponentially on 1/ε. The algorithm can be generalized to the budgeted unique unit-disk coverage problem in which each point has a profit, each disk 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 - Approximation algorithm

KW - Computational geometry

KW - Unique coverage problem

KW - Unit disk

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U2 - 10.1016/j.tcs.2014.04.014

DO - 10.1016/j.tcs.2014.04.014

M3 - Article

AN - SCOPUS:84926689043

VL - 544

SP - 14

EP - 31

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - C

ER -