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The Largest Empty Annulus Problem [chapter]

J. M. Díaz-Báñez, F. Hurtado, H. Meijer, D. Rappaport, T. Sellares
2002 Lecture Notes in Computer Science  
Given a set of n points S in the Euclidean plane, we address the problem of computing an annulus A, (open region between two concentric circles) of largest width, that partitions S into a subset of points  ...  This problem can be considered as a maximin facility location problem for n points such that the facility is a circumference.  ...  Finding a largest empty annulus We describe an algorithm to determine the centre of a largest empty annulus that is constrained to lie on the right bisector of a pair of points p and q, B(p, q).  ... 
doi:10.1007/3-540-47789-6_5 fatcat:sw67cskxbrglvcv2krk3e6vpzi

THE LARGEST EMPTY ANNULUS PROBLEM

J. M. DÍAZ-BÁÑEZ, F. HURTADO, H. MEIJER, D. RAPPAPORT, J. A. SELLARÈS
2003 International journal of computational geometry and applications  
Given a set of n points S in the Euclidean plane, we address the problem of computing an annulus A, (open region between two concentric circles) of largest width, that partitions S into a subset of points  ...  This problem can be considered as a maximin facility location problem for n points such that the facility is a circumference.  ...  Finding a largest empty annulus We describe an algorithm to determine the centre of a largest empty annulus that is constrained to lie on the right bisector of a pair of points p and q, B(p, q).  ... 
doi:10.1142/s0218195903001207 fatcat:i2risglin5gelp7d3jpsokun54

On the Minimum-Area Rectangular and Square Annulus Problem [article]

Sang Won Bae
2019 arXiv   pre-print
The same approach is shown to apply also to the minimum-width square annulus problem and the largest empty square problem over all orientations, resulting in O(n^3)-time algorithms for both problems.  ...  For a fixed orientation, we show reductions to well-studied problems: the minimum-width square annulus problem and the largest empty rectangle problem, yielding algorithms of time complexity O(n^2 n) and  ...  problems, such as the minimum-width annulus problem and the largest empty rectangle problem.  ... 
arXiv:1904.06832v1 fatcat:3ii26l4lsjh6rnd3vt3bdmjnbq

On the Minimum-Area Rectangular and Square Annulus Problem

Sang Won Bae
2020 Computational geometry  
For a fixed orientation, we show reductions to well-studied problems: the minimum-width square annulus problem and the largest empty rectangle problem, yielding algorithms of time complexity O (n log 2  ...  In arbitrary orientation, we present O (n 3 )-time algorithms for the rectangular and square annulus problem by enumerating all maximal empty rectangles over all orientations.  ...  annulus problem and the largest empty rectangle problem are reduced to each other in linear time.  ... 
doi:10.1016/j.comgeo.2020.101697 fatcat:itttxkdykfbk5katebtc7jzzd4

Locating an obnoxious plane

J.M. Díaz-Báñez, M.A. López, J.A. Sellarès
2006 European Journal of Operational Research  
Finally, we show how to adapt our method for computing a largest empty annulus in the plane, improving the known time bound O(n 3 log n) [8] .  ...  In a geometric setting, the problem asks for the widest empty slab through n points in space, where a slab is the open region of IR 3 that is bounded by two parallel planes that intersect the convex hull  ...  The second author was supported in part by the National Science Foundation under grant DMS-0107628. The third author was supported in part by grants TIC2001-2392-C03-01.  ... 
doi:10.1016/j.ejor.2005.02.048 fatcat:ldwgirejirab5p5ipqfjnnchue

Maximum-Width Empty Square and Rectangular Annulus [article]

Sang Won Bae, Arpita Baral, Priya Ranjan Sinha Mahapatra
2018 arXiv   pre-print
The maximum-width empty annulus problem asks to find an annulus of a certain shape with the maximum possible width that avoids a given set of n points in the plane.  ...  In this paper, we study square and rectangular variants of the maximum-width empty anuulus problem, and present first nontrivial algorithms.  ...  There has been a little work on the maximum-width empty annulus problem. Díaz-Báñez et al.  ... 
arXiv:1811.06217v1 fatcat:rh4usx6hwra4hcjq6um5yt7z6y

Tight lower bounds for connected queen domination problems on the chessboard [article]

Sneha S. Venkatesan, S. M. Venkatesan
2016 arXiv   pre-print
We also discuss extensions of the connected domination problem and additional directions.  ...  We first show a lower bound of 2N/3-1 for the connected minimum queen domination (or cover) problem on the NXN chessboard - the upper bound is only 2 higher at most and is easy to show. 2.  ...  Also, let (y 1 + 1) and (N − y 2 ) be the smallest and the largest-indexed empty rows respectively.  ... 
arXiv:1608.02531v1 fatcat:kxl2zhq4krc2pdjep7fzk5deiy

Empty Squares in Arbitrary Orientation Among Points

Sang Won Bae, Sang Duk Yoon, Danny Z. Chen, Sergio Cabello
2020 International Symposium on Computational Geometry  
Several new algorithmic results are also obtained: a largest empty square among P and a square annulus of minimum width or minimum area that encloses P over all orientations can be computed in worst-case  ...  This paper studies empty squares in arbitrary orientation among a set P of n points in the plane.  ...  The problem of finding a largest empty square is a square variant of the well-known largest empty rectangle problem.  ... 
doi:10.4230/lipics.socg.2020.13 dblp:conf/compgeom/BaeY20 fatcat:dqffcalnovbmfffwvif2kqkk7i

Page 292 of Mathematical Reviews Vol. 20, Issue 3 [page]

1959 Mathematical Reviews  
The problem is related to the corresponding problem for the circle by showing that /=¢(y(z)), where p is a specified map of the annulus on the circle, and ¢ the solution of the Milloux problem for the  ...  Let |w|<d* be the largest disc contained in the map of |z|<1, and |w|<d® be the largest disc contained in the map of |z/S7o, where |z|Sro is the largest disc of convex mapping.  ... 

O(n 3logn) Time Complexity for the Optimal Consensus Set Computation for 4-Connected Digital Circles [chapter]

Gaelle Largeteau-Skapin, Rita Zrour, Eric Andres
2013 Lecture Notes in Computer Science  
, while fixing the thickness.  ...  This paper presents a method for fitting 4-connected digital circles to a given set of points in 2D images in the presence of noise by maximizing the number of inliers, namely the optimal consensus set  ...  The work for this paper was partly financed by Egide, franco-Japanese PHC Sakura project n 27608XJ and by the Poitou Charentes region project n 11/RPC-R-051.  ... 
doi:10.1007/978-3-642-37067-0_21 fatcat:3qwfe2ykzbgv5aklcu3tbmcj3q

Empty Squares in Arbitrary Orientation Among Points [article]

Sang Won Bae, Sang Duk Yoon
2019 arXiv   pre-print
Several new algorithmic results are also obtained: a largest empty square among P and a square annulus of minimum width or minimum area that encloses P over all orientations can be computed in worst-case  ...  This paper studies empty squares in arbitrary orientation among a set P of n points in the plane.  ...  The problem of finding a largest empty square is a square variant of the well-known largest empty rectangle problem.  ... 
arXiv:1911.12988v1 fatcat:fnth6xbhiveqzib5psqefwcdgm

Optimizing a constrained convex polygonal annulus

Gill Barequet, Prosenjit Bose, Matthew T. Dickerson, Michael T. Goodrich
2005 Journal of Discrete Algorithms  
For all of these problems, we solve for the cases where smallest and largest are defined by either the offsetting or scaling of a polygon.  ...  In the variants that we address the size of the polygon defining the inner (respectively, outer) boundary of the annulus is fixed, and the annulus is minimized by minimizing (respectively, maximizing)  ...  Acknowledgements The authors wish to thank Amy Briggs, Iuliana Marinov, and Jelena Ignjatovic for work on the implementations reported in Appendix A.  ... 
doi:10.1016/j.jda.2003.12.004 fatcat:suqjchhkyzeljpfavzrsi625am

Optimal Consensus Set for nD Fixed Width Annulus Fitting [chapter]

Rita Zrour, Gaelle Largeteau-Skapin, Eric Andres
2015 Lecture Notes in Computer Science  
This paper presents a method for fitting a nD fixed width spherical shell to a given set of nD points in an image in the presence of noise by maximizing the number of inliers, namely the consensus set.  ...  We present an algorithm, that provides the optimal solution(s) within a time complexity O(N n+1 log N ) for dimension n, N being the number of points.  ...  Acknowledgments The authors express their thanks to Mr. Pierre Boulenguez, who contributed in the implementation of a part of the 3D Fitting.  ... 
doi:10.1007/978-3-319-26145-4_8 fatcat:hc2knpvncrgbra6rzda67yregi

Efficient Broadcast on Random Geometric Graphs [chapter]

Milan Bradonjić, Robert Elsässer, Tobias Friedrich, Thomas Sauerwald, Alexandre Stauffer
2010 Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms  
This result has independent interest and, in particular, gives that the diameter of the largest connected component of an RGG is Θ( √ n /r), which surprisingly has been an open problem so far.  ...  We analyze the following randomized broadcast algorithm on RGGs. At the beginning, only one node from the largest connected component of the RGG is informed.  ...  Part of this work was funded through the Laboratory Directed Research and Development Program, and Center for Nonlinear Studies.  ... 
doi:10.1137/1.9781611973075.114 dblp:conf/soda/BradonjicEFSS10 fatcat:rnvu74zjyraclmzrt4eh3zgk7u

Thermal-viscous instabilities in the accretion disk of GRS 1915+105 [article]

T. Belloni, M. Mendez, A.R. King (University of Leicester), M. van der Klis, J. van Paradijs
1997 arXiv   pre-print
disk around the compact object, followed by a slower re-filling of the emptied region.  ...  The duration of an event and the size of the disappearing region fit remarkably well the expected radius dependence of the viscous time scale for the radiation-pressure dominated region of an accretion  ...  emptied section of the disk.  ... 
arXiv:astro-ph/9712170v1 fatcat:zggpzahxhjguhei35f47ds7cza
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