Maximum-width rainbow-bisecting empty annulus
Given a set of n colored points with k colors in the plane, we study the problem of computing a maximum-width rainbow-bisecting empty annulus (of objects specifically axis-parallel square, axis-parallel rectangle and circle) problem. We call a region rainbow if it contains at least one point of each...
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| Veröffentlicht in: | Computational geometry : theory and applications Jg. 120; S. 102088 |
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Elsevier B.V
01.06.2024
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| Abstract | Given a set of n colored points with k colors in the plane, we study the problem of computing a maximum-width rainbow-bisecting empty annulus (of objects specifically axis-parallel square, axis-parallel rectangle and circle) problem. We call a region rainbow if it contains at least one point of each color. The maximum-width rainbow-bisecting empty annulus problem asks to find an annulus A of a particular shape with maximum possible width such that A does not contain any input points and it bisects the input point set into two parts, each of which is a rainbow. We compute a maximum-width rainbow-bisecting empty axis-parallel square, axis-parallel rectangular and circular annulus in O(n3) time using O(n) space, in O(k2n2logn) time using O(nlogn) space and in O(n3) time using O(n2) space respectively. |
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| AbstractList | Given a set of n colored points with k colors in the plane, we study the problem of computing a maximum-width rainbow-bisecting empty annulus (of objects specifically axis-parallel square, axis-parallel rectangle and circle) problem. We call a region rainbow if it contains at least one point of each color. The maximum-width rainbow-bisecting empty annulus problem asks to find an annulus A of a particular shape with maximum possible width such that A does not contain any input points and it bisects the input point set into two parts, each of which is a rainbow. We compute a maximum-width rainbow-bisecting empty axis-parallel square, axis-parallel rectangular and circular annulus in O(n3) time using O(n) space, in O(k2n2logn) time using O(nlogn) space and in O(n3) time using O(n2) space respectively. |
| ArticleNumber | 102088 |
| Author | Bae, Sang Won Baral, Arpita Yoon, Sang Duk Banerjee, Sandip Mahapatra, Priya Ranjan Sinha |
| Author_xml | – sequence: 1 givenname: Sang Won surname: Bae fullname: Bae, Sang Won organization: Division of Computer Science and Engineering, Kyonggi University, Korea – sequence: 2 givenname: Sandip surname: Banerjee fullname: Banerjee, Sandip email: sandip.ndp@gmail.com organization: IDSIA, USI-SUPSI, Lugano, Switzerland – sequence: 3 givenname: Arpita surname: Baral fullname: Baral, Arpita organization: Department of Computer Science and Engineering, NSHM Knowledge Campus (Group of Institutions), Durgapur, India – sequence: 4 givenname: Priya Ranjan Sinha surname: Mahapatra fullname: Mahapatra, Priya Ranjan Sinha organization: Department of Computer Science and Engineering, University of Kalyani, India – sequence: 5 givenname: Sang Duk surname: Yoon fullname: Yoon, Sang Duk organization: Department of Service and Design Engineering, Sungshin Women's University, Korea |
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| Cites_doi | 10.1016/j.dam.2018.02.014 10.1142/S0218195909003076 10.1016/j.ejor.2005.02.048 10.1016/0022-0000(89)90038-X 10.1016/j.comgeo.2021.101747 10.1142/S0218195903001207 10.1016/j.tcs.2012.02.041 10.1016/j.tcs.2017.11.031 10.1016/0020-0190(96)00070-1 10.1016/j.dam.2018.05.011 10.1016/j.ipl.2006.02.002 |
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