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The one-round weighted Voronoi Game

Zeinab Hassani, Bahram Sadeghi Bigham, Marzieh Eskandari
2012 Zenodo  
In this paper a new version of one-round Voronoi game is presented in which multiplicatively weighted Voronoi diagram is used.  ...  It is showed in this paper when two players have same points, there is a winning strategy for one of the players. Also we discuss on one dimensional spaces.  ...  We present the one-round Voronoi game with multiplicatively weighted Voronoi diagrams in a one-dimensional. Region like a highway.  ... 
doi:10.5281/zenodo.4826271 fatcat:vntnaplhgffmnccflpc6iraojy

The one- round weighted Voronoi Game

Bahram Sadeghi Bigham Zeinab Hassani
2012 Zenodo  
In this paper a new version of one-round Voronoi game is presented in which multiplicatively weighted Voronoi diagram is used.  ...  It is showed in this paper when two players have same points, there is a winning strategy for one of the players. Also we discuss on one dimensional spaces.  ...  We present the one-round Voronoi game with multiplicatively weighted Voronoi diagrams in a one-dimensional. Region like a highway.  ... 
doi:10.5281/zenodo.3783847 fatcat:2sycq2kox5ah5kdczuazzgn2li

Capacity-Constrained Voronoi Diagrams in Continuous Spaces

Michael Balzer
2009 2009 Sixth International Symposium on Voronoi Diagrams  
Our second approach is based on weighted distance functions and optimizes the weights of the sites.  ...  A capacityconstrained Voronoi diagram is a partition in which the area for each Voronoi region is predefined.  ...  weighted Voronoi diagram V (S,W,C) Initialize a set of n weights W := {0, . . . , weight w such that δ c (w, i) , and not on the global function D.  ... 
doi:10.1109/isvd.2009.28 dblp:conf/isvd/Balzer09 fatcat:fbpcetm45bgn3p2jwvf4x5rivu

APPLICATION OF THE THEORY OF OPTIMAL SET PARTITIONING BEFORE BUILDING MULTIPLICATIVELY WEIGHTED VORONOI DIAGRAM WITH FUZZY PARAMETERS

O.M. Kiseliova, O.M. Prytomanova, V.H. Padalko
2020 EurasianUnionofScientists  
An algorithm for constructing a multiplicatively weighted Voronoi diagram involving fuzzy parameters with the optimal location of a finite number of generator points in a limited set of n-dimensional Euclidean  ...  The algorithm has been developed based on the synthesis of methods of solving the problems of optimal set partitioning theory involving neurofuzzy technologies modifications of N.Z.  ...  Growing crystals is one of the illustrative ways of obtaining a multiplicatively weighted Voronoi diagram [6] .  ... 
doi:10.31618/esu.2413-9335.2020.6.71.615 fatcat:f5jxyhai4jespeytqniwolsa3m

Dynamic weighted Voronoi diagrams and weighted minimax matching of two corresponding point sets

Keiko Imai, Hiroshi Imai
1998 Optimization Methods and Software  
For this weighted geometric fitting problem, dynamic weighted Voronoi diagrams have been applied to obtain an almost cubic algorithm.  ...  A weighted geometric fitting problem between two corresponding sets of points is to minimize the maximum weighted distance between two corresponding pairs of points by translating and rotating one set  ...  Acknowledgment The authors would like to thank both referees for their valuable comments on the original version of this paper.  ... 
doi:10.1080/10556789808805714 fatcat:lbnksjjkdjhlrcwjh7opqenf5u

On Dynamic Generalized Voronoi Diagrams in the Euclidean Metric [chapter]

M. L. Gavrilova, J. Rokne
2001 Lecture Notes in Computer Science  
The problem of dynamic maintenance of the Voronoi diagram for a set of spheres moving independently in d-dimensional space is addressed in this paper.  ...  The maintenance of the generalized Voronoi diagram of spheres, moving alone the given trajectories, requires the calculation of topological events, that occur when d + 2 spheres become tangent to a common  ...  Following the classification of generalized Voronoi diagrams presented in [14] the Euclidean weighted Voronoi diagram is an instance of the class of additively weighted Voronoi diagrams, where d(x, P  ... 
doi:10.1007/3-540-45545-0_78 fatcat:fastbknewfempg55mgewsvvthy

High-Dimensional Power Diagrams for Semi-Discrete Optimal Transport

Philip Claude Caplan
2021 Zenodo  
the power diagram (Laguerre diagram) in higher dimensions.  ...  Recent algorithms have been developed for solving the semi-discrete problem in 2d and 3d, however, algorithms in higher dimensions have yet to be demonstrated, which rely on the efficient calculation of  ...  Voronoi diagram when the weights are all zero.  ... 
doi:10.5281/zenodo.5559221 fatcat:cvfb5ssxene6rd67fjggpesjg4

Constructing Two-Dimensional Voronoi Diagrams via Divide-and-Conquer of Envelopes in Space [chapter]

Ophir Setter, Micha Sharir, Dan Halperin
2010 Lecture Notes in Computer Science  
The framework is sufficiently general to support diagrams embedded on a family of two-dimensional parametric surfaces in R^3.  ...  We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions.  ...  and support of this work. random point sets it is known that the expected number of intersections between the farthest and the nearest Voronoi diagrams is linear.  ... 
doi:10.1007/978-3-642-16007-3_1 fatcat:6yorbvghgfdsle3celaedfdn2i

Discrete Sibson interpolation

S.W. Park, L. Linsen, O. Kreylos, J.D. Owens, B. Hamann
2006 IEEE Transactions on Visualization and Computer Graphics  
The main reason for both problems is the method's implementation based on a Voronoi diagram of all data points.  ...  platform to scholars worldwide. a Voronoi diagram of all data points.  ...  The two-dimensional test case is based on a Voronoi diagram on a 512 Â 512 pixel grid, and the three-dimensional test case is based on a 128 Â 128 Â 128 voxel grid using m randomly generated sites.  ... 
doi:10.1109/tvcg.2006.27 pmid:16509383 fatcat:axbd4w2crvckrn6gasjswxb3di

Constructing Two-Dimensional Voronoi Diagrams via Divide-and-Conquer of Envelopes in Space

Ophir Setter, Micha Sharir, Dan Halperin
2009 2009 Sixth International Symposium on Voronoi Diagrams  
However, the framework is sufficiently general to support diagrams embedded on a family of two-dimensional parametric surfaces in R 3 .  ...  We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. Most diagrams mentioned in the paper are in the plane.  ...  and support of this work. random point sets it is known that the expected number of intersections between the farthest and the nearest Voronoi diagrams is linear.  ... 
doi:10.1109/isvd.2009.20 dblp:conf/isvd/SetterSH09 fatcat:pexovgtyq5e4fazlbxxp4ylnpa

Application of Rank Sequence Localization Algorithm based on Voronoi and Spearman in WSN

XuJian Wei, Wang Dan
2014 International Journal of Smart Home  
WSN localization algorithm by introducing related concept of Spearman rank, uses the spatial division methods of Voronoi diagram and sequence localization ideas, relies on the import of virtual anchor  ...  First of all, the paper divides the localization space of WSN according to the Voronoi diagram, takes the polygon's points, center of gravity and the boundary intersection as virtual anchor nodes, and  ...  Construction of Two-Dimensional Voronoi Diagram During the process of Voronoi division, the center of gravity's coordinate of the anchor nodes is the vertex of Voronoi polygon, and the coordinate of boundary  ... 
doi:10.14257/ijsh.2014.8.6.10 fatcat:gh7ulxs2r5b53l3lpqyvcstvm4

Apollonius diagrams and the Representation of Sounds and Music

Alex McLean, Frederic Fol Leymarie, Geraint Wiggins
2007 4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)  
We introduce the use of weighted medial graph structures to represent sounds and musical events.  ...  The use of colour, modulation (of waveforms), orientation, speed, etc., allows us to integrate multiple musical features in our dynamic diagrams.  ...  Whether such a simplification is acceptable depends on the context, but we introduce a system for constructing a Voronoi diagram with individually weighted sites in Section 4.2.  ... 
doi:10.1109/isvd.2007.7 dblp:conf/isvd/McLeanLW07 fatcat:2a6xxfxlcvcjznxexc6oh4jmd4

Computing Voronoi Treemaps: Faster, Simpler, and Resolution-independent

Arlind Nocaj, Ulrik Brandes
2012 Computer graphics forum (Print)  
(3) Voronoi diagram (power diagram with zero weights).  ...  cell area, weighted Voronoi diagrams can be used.  ... 
doi:10.1111/j.1467-8659.2012.03078.x fatcat:mc33x44dxzfsngifrufaci5awq

On the conversion of ordinary voronoi diagrams into laguerre diagrams

Francois Anton, Darka Mioc
1999 Canadian Conference on Computational Geometry  
We present some geometric relationships between the ordinary Voronoi diagram, and the Voronoi diagram in the Laguerre geometry.  ...  W e derive from these properties an algorithm for the conversion of ordinary Voronoi diagrams into Voronoi diagrams in the Laguerre geometry.  ...  They are weighted Voronoi diagrams based on a metric di erent from the Euclidean distance: the power of a point relatively to a weight circle.  ... 
dblp:conf/cccg/AntonM99 fatcat:na64hl2dgnfxxi3hnm22pvqc5y

Tsunami wave propagation by voronoi diagram

V Yuvaraj, S Rajasekaran, D Nagarajan
2018 International Journal of Engineering & Technology  
It involves the Introduction of voronoi diagram in tsunami wave propagation with the help of a fast-marching method to find the spread of the tsunami waves in the coastal regions.  ...  This analytical method gives the horizontal and vertical layers of the wave run up and enables the calculation of reaching time.  ...  The wave spread region in the ocean is considered as the finite dimensional space. the weighted voronoi cell is executed for the three-dimensional space [17] .  ... 
doi:10.14419/ijet.v7i3.12486 fatcat:6jztvhvfu5ee7fp5gmomle46yi
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