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https://hdl.handle.net/10119/13802
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| Title: | A 4.31-Approximation for the Geometric Unique Coverage Problem on Unit Disks |
| Authors: | Ito, Takehiro
Nakano, Shin-ichi
Okamoto, Yoshio
Otachi, Yota
Uehara, Ryuhei
Uno, Takeaki
Uno, Yushi |
| Keywords: | approxiamtion algorithm
computational geometry
unique coverage problem
unit disk |
| Issue Date: | 2014-08-07 |
| Publisher: | Elsevier |
| Magazine name: | Theoretical Computer Science |
| Volume: | 544 |
| Start page: | 14 |
| End page: | 31 |
| DOI: | 10.1016/j.tcs.2014.04.014 |
| Abstract: | 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 totalprofit of the uniquely covered points under the condition that the total cost is at most a given bound. |
| Rights: | Copyright (C)2014, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International license (CC BY-NC-ND 4.0). [http://creativecommons.org/licenses/by-nc-nd/4.0/] NOTICE: This is the author's version of a work accepted for publication by Elsevier. Takehiro Ito, Shin-ichi Nakano, Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno, and Yushi Uno, Theoretical Computer Science, 544, 2014, 14-31, http://dx.doi.org/10.1016/j.tcs.2014.04.014 |
| URI: | https://hdl.handle.net/10119/13802 |
| Material Type: | author |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
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