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).
Publisher Copyright:
© 2014 Elsevier B.V.
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 -