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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/13835

Title: A polynomial-time approximation scheme for the geometric unique coverage problem on unit squares
Authors: Ito, Takehiro
Nakano, Shin-ichi
Okamoto, Yoshio
Otachi, Yota
Uehara, Ryuhei
Uno, Takeaki
Uno, Yushi
Keywords: unit-square coverage problem
polynomial time approximation scheme
computational goemetry
Issue Date: 2016-01
Publisher: Elsevier
Magazine name: Computational Geometry: Theory and Applications
Volume: 51
Start page: 25
End page: 39
DOI: 10.1016/j.comgeo.2015.10.004
Abstract: 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.
Rights: Copyright (C)2016, 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. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Takehiro Ito, Shin-ichi Nakano, Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno, and Yushi Uno, Computational Geometry: Theory and Applications, 51, 2016, 25-39, http://dx.doi.org/10.1016/j.comgeo.2015.10.004
URI: http://hdl.handle.net/10119/13835
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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