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MAXIMIZING A VORONOI REGION: THE CONVEX CASE

FRANK DEHNE, ROLF KLEIN, RAIMUND SEIDEL
2005 International journal of computational geometry and applications  
Given a set S of s points in the plane, where do we place a new point, p, in order to maximize the area of its region in the Voronoi diagram of S and p?  ...  We study the case where the Voronoi neighbors of p are in convex position, and prove that there is at most one local maximum.  ...  The authors would like to thank the following colleagues for fruitful discussions: Franz Aurenhammer, Otfried Cheong, Horst Hamacher, Christian Icking, Elmar Langetepe, Lihong Ma, Kurt Mehlhorn, Belen  ... 
doi:10.1142/s0218195905001786 fatcat:ohurlqtez5fexiqmtut2wahkr4

Maximizing Voronoi Regions of a Set of Points Enclosed in a Circle with Applications to Facility Location

Bhaswar B. Bhattacharya
2010 Journal of Mathematical Modelling and Algorithms  
In this paper we introduce an optimization problem, which involves maximization of the area of Voronoi regions of a set of points placed inside a circle.  ...  We also consider another variation of this problem where a set of n points is placed inside ψ, and the task is to locate a new point q inside ψ such that the area of the Voronoi region of q is maximized  ...  The author is also grateful to the two anonymous referees for their critical comments, which have greatly improved the quality of the paper.  ... 
doi:10.1007/s10852-010-9142-0 fatcat:6ekobpgv4jb2zi4l5xwhwh2aqe

Robot navigation in unknown terrains using learned visibility graphs. Part I: The disjoint convex obstacle case

B. Oommen, S. Iyengar, N. Rao, R. Kashyap
1987 IEEE Journal on Robotics and Automation  
An algorithm is presented to navigate a robot in an unexplored terrain that is arbitrarily populated with disjoint convex polygonal obstacles in the plane.  ...  In this case, the process of navigation involves both learning the information about the obstacle terrain and path planning.  ...  Lazano-Perez of the Massachusetts Institute of Technology for carefully reading the manuscript and for his helpful and critical comments. He also suggested various  ... 
doi:10.1109/jra.1987.1087133 fatcat:e3vwpvz45jcmbflw2qv42rgrsm

Visibility-oriented coverage control of mobile robotic networks on non-convex regions

Yiannis Kantaros, Michalis Thanou, Anthony Tzes
2014 2014 IEEE International Conference on Robotics and Automation (ICRA)  
Index Terms-Non-convex area coverage problem,visibilitybased Voronoi diagrams,mobile robotic networks  ...  A gradient-ascent control law is proposed, based on visibility-based Voronoi diagrams, leading the network to the optimal final state in terms of total area coverage.  ...  The authors in [14, 15] present a technique for transforming a class of non-convex regions into convex ones using a diffeomorphism.  ... 
doi:10.1109/icra.2014.6906995 dblp:conf/icra/KantarosTT14 fatcat:7qvws5qagfawplouuot4tjoza4

GPU-Based Influence Regions Optimization [chapter]

Marta Fort, J. Antoni Sellarès
2012 Lecture Notes in Computer Science  
living/working in the region having the plant among their 3-farthest garbage dumps is maximum.  ...  of people living/working in the region having the new restaurant among their 4-nearest restaurants is maximum.  ...  A. Dehne, Rolf Klein, and Raimund Seidel, Maximizing a Voronoi region: the convex case, Int. J. Comput.  ... 
doi:10.1007/978-3-642-31125-3_20 fatcat:7nc563fjivbp3dr2w33ocvjeie

POLYLLA: Polygonal meshing algorithm based on terminal-edge regions [article]

Sergio Salinas, Nancy Hitschfeld-Kahler, Alejandro Ortiz-Bernardin, Hang Si
2022 arXiv   pre-print
Each polygon is built from a terminal-edge region surrounded by edges that are not the longest-edge of any of the two triangles that share them.  ...  The final mesh contains polygons with convex and non convex shape.  ...  It is known that Delaunay triangulations are the ones that maximize the smallest angle among all the triangulations of a point set.  ... 
arXiv:2201.11925v2 fatcat:626lrmnavzhgjo4zadvufpjhfy

Voronoi regions for binary linear block codes

E. Agrell
1996 IEEE Transactions on Information Theory  
The Voronoi regions of a block code govern many aspects of the code's performance on a Gaussian channel, and they are fundamental instruments in, for example, error probability analysis and soft decision  ...  This paper presents an efficient method to find the boundaries of the Voronoi regions for an arbitrary binary linear block code. Two theoretical results together lead to the Voronoi regions.  ...  ACKNOWLEDGMENTS The author would like to thank Per Hedelin, Stefan Dodunekov, and Mikael Skoglund, whose helpful comments led to significant improvements of this paper.  ... 
doi:10.1109/18.481810 fatcat:iafwc4ij55gpdawck5r4b62ptm

Algorithms for regional source localization

Sandra H. Dandach, Francesco Bullo
2009 2009 American Control Conference  
In this paper we use the MAP criterion to locate a region containing a source.  ...  We also study the geometric properties of the model that make it possible in some situations to detect the correct region with a unique sensor.  ...  This would not have been the case with two sensors with general convex regions. In general, the noise will not be vanishing and the decision needs to be made with a finite number of measurements.  ... 
doi:10.1109/acc.2009.5160291 dblp:conf/amcc/DandachB09 fatcat:nqyrvlf7grdmnd27qxuqdxqaka

Querying Approximate Shortest Paths in Anisotropic Regions

Siu-Wing Cheng, Hyeon-Suk Na, Antoine Vigneron, Yajun Wang
2010 SIAM journal on computing (Print)  
Our data structure returns a (1 + ε) approximation of the shortest path cost from the fixed source to a query destination in O(log ρn ε ) time.  ...  Distances in each face of this subdivision are measured by a possibly asymmetric convex distance function whose unit disk is contained in a concentric unit Euclidean disk, and contains a concentric Euclidean  ...  By breaking ties in a "lexicographical manner" [8] , Ma [10] showed that if the distance function is defined by a convex polygon of K sides, then the Voronoi regions are star-shaped and every bisector  ... 
doi:10.1137/080742166 fatcat:7viszjf23nbalimjkisgfwddcy

Querying approximate shortest paths in anisotropic regions

Siu-Wing Cheng, Hyeon-Suk Na, Antoine Vigneron, Yajun Wang
2007 Proceedings of the twenty-third annual symposium on Computational geometry - SCG '07  
Our data structure returns a (1 + ε) approximation of the shortest path cost from the fixed source to a query destination in O(log ρn ε ) time.  ...  Distances in each face of this subdivision are measured by a possibly asymmetric convex distance function whose unit disk is contained in a concentric unit Euclidean disk, and contains a concentric Euclidean  ...  By breaking ties in a "lexicographical manner" [8] , Ma [10] showed that if the distance function is defined by a convex polygon of K sides, then the Voronoi regions are star-shaped and every bisector  ... 
doi:10.1145/1247069.1247082 dblp:conf/compgeom/ChengNVW07 fatcat:mondss74irfsldcq33ttu5gjcq

Algorithms for regional source localization [article]

S. H. Dandach, F. Bullo
2009 arXiv   pre-print
In this paper we use the MAP criterion to locate a region containing a source.  ...  We also study the geometric properties of the model that make it possible in some situations to detect the correct region with a unique sensor.  ...  This would not have been the case with two sensors with general convex regions. In general, the noise will not be vanishing and the decision needs to be made with a finite number of measurements.  ... 
arXiv:0903.3061v1 fatcat:yp7cp2a4cva6llxrku62qpwo7e

Efficient algorithm for placing a given number of base stations to cover a convex region

Gautam K. Das, Sandip Das, Subhas C. Nandy, Bhabani P. Sinha
2006 Journal of Parallel and Distributed Computing  
We develop an efficient algorithm for this problem using Voronoi diagram which works for covering a convex region of arbitrary shape.  ...  The objective is to place a given number of base-stations in a given convex region, and to assign range to each of them such that every point in the region is covered by at least one base-station, and  ...  In our case, the set of demand points D is the entire convex region under consideration, and the problem is referred to as a covering problem in the literature.  ... 
doi:10.1016/j.jpdc.2006.05.004 fatcat:5d4njporwjfexabwopmm3wzf2a

Algorithms for Finding Vulnerabilities and Deploying Additional Sensors in a Region with Obstacles

Kibeom Kim, Sunggu Lee
2021 Electronics  
Consider a two-dimensional rectangular region guarded by a set of sensors, which may be smart networked surveillance cameras or simpler sensor devices.  ...  for the minimum exposure path in a systematic manner.  ...  Data Availability Statement: The data presented in this study are available in supplementary materials. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/electronics10121504 fatcat:bfuzuufzjvg4vg4vkezqq44bsy

Top-k diversity queries over bounded regions

Ilio Catallo, Eleonora Ciceri, Piero Fraternali, Davide Martinenghi, Marco Tagliasacchi
2013 ACM Transactions on Database Systems  
region.  ...  The goal is to provide a good quality result set in terms of both relevance and diversity.  ...  The point x * ∈ Z that maximizes the minimum distance from all the points in X is a vertex of the convex hull of P i ∖ D, where P i is one of the cells of Vor(X , U).  ... 
doi:10.1145/2487259.2487262 fatcat:nmbifmsvlbgzxfzvp6da34pm7m

Active Contours for Multi-region Image Segmentation with a Single Level Set Function [chapter]

Anastasia Dubrovina, Guy Rosman, Ron Kimmel
2013 Lecture Notes in Computer Science  
We propose a novel approach to tackle the problem of multiple-region segmentation for an arbitrary number of regions.  ...  Yet, unlike most existing methods, evolution is executed using a single non-negative level set function, through the Voronoi Implicit Interface Method for a multi-phase interface evolution.  ...  Acknowledgements The authors thank J.A. Sethian of UC Berkeley for intriguing discussions and introducing the VIIM to our group.  ... 
doi:10.1007/978-3-642-38267-3_35 fatcat:6i7yoacqsvblhdddfn7l45foum
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