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Computation of Spatial Skyline Points [article]

Binay Bhattacharya, Arijit Bishnu, Otfried Cheong, Sandip Das, Arindam Karmakar, Jack Snoeyink
2019 arXiv   pre-print
We reduce this problem of determining non-dominated sites to the problem of finding sites that have non-empty cells in an additively weighted Voronoi diagram under a convex distance function.  ...  We discuss a method of finding skyline or non-dominated sites in a set P of n point sites with respect to a set S of m points.  ...  The key idea is to represent the union of the cones using the compact representation of Voronoi diagrams by McAllister et al.  ... 
arXiv:0909.0814v2 fatcat:g4eg4ccre5fmlksxpg4qenur2a

Voronoi diagrams for polygon-offset distance functions [chapter]

Gill Barequet, Matthew T. Dickerson, Michael T. Goodrich
1997 Lecture Notes in Computer Science  
In this paper we develop the concept of a polygon-o set distance function and show how to compute the respective nearest-and furthest-site Voronoi diagrams of point sites in the plane.  ...  We provide optimal deterministic O(n(log n + log m) + m)-time algorithms, where n is the number of points and m is the complexity of the underlying polygon, for computing compact representations of both  ...  Bose for helpful discussions on Voronoi diagrams. We also thank V. Mirelli for introducing us the concept of polygon o sets and their applications.  ... 
doi:10.1007/3-540-63307-3_60 fatcat:y5loxmfovvgxfbrlxe5yhbs2jy

Anomaly Detection with the Voronoi Diagram Evolutionary Algorithm [chapter]

Luis Martí, Arsene Fansi-Tchango, Laurent Navarro, Marc Schoenauer
2016 Lecture Notes in Computer Science  
From the union of P t and P off , the best n pop are selected using the non-dominated sorting selection of NSGA-II [3] . This process repeats until the stopping criterion of the algorithm is met.  ...  Any set of points, known as Voronoi sites, in a given n-dimensional Euclidean space E defines a Voronoi diagram, i.e., a partition of that space into Voronoi cells: the cell corresponding to a given site  ... 
doi:10.1007/978-3-319-45823-6_65 fatcat:oxyten7qejaafapgljfk5zffq4

Compact Voronoi Diagrams for Moving Convex Polygons [chapter]

Leonidas J. Guibas, Jack Snoeyink, Li Zhang
2000 Lecture Notes in Computer Science  
We use a compact diagram for the polygons, dual to the Voronoi, first presented in [MKS96] .  ...  This compact Voronoi diagram can be used for collision detection or retraction motion planning among the moving polygons.  ...  Combinatorial changes of the compact Voronoi diagram In this section, we will study the number of combinatorial changes of the compact Voronoi diagram.  ... 
doi:10.1007/3-540-44985-x_30 fatcat:bb63fodayja6xipo7jclv7ylhm

Voronoi Diagram for Convex Polygonal Sites with Convex Polygon-Offset Distance Function [chapter]

Gill Barequet, Minati De
2017 Lecture Notes in Computer Science  
Using this notion of point-to-point distance, they showed how to compute the corresponding nearest-and farthest-site Voronoi diagram for a set of points.  ...  We show that the combinatorial complexity of the nearest-site Voronoi diagram of n disjoint line segments is O(nm), which is asymptotically equal to that of the Voronoi diagram of n point sites with respect  ...  [14] presented an algorithm to compute a compact representation of the diagram in O(k log n) time using only O(k) space.  ... 
doi:10.1007/978-3-319-53007-9_3 fatcat:gehwj7jhvnhslngraji5rfj6me

Zone diagrams in compact subsets of uniformly convex normed spaces

Eva Kopecká, Daniel Reem, Simeon Reich
2011 Israel Journal of Mathematics  
A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams.  ...  In the present paper we prove the existence of zone diagrams with respect to finitely many pairwise disjoint compact sites contained in a compact and convex subset of a uniformly convex normed space, provided  ...  Acknowledgements We thank Akitoshi Kawamura, Jiří Matoušek, and Takeshi Tokuyama for providing a copy of their recent paper [14] before posting it on the arXiv, Orr Shalit for a useful suggestion, and  ... 
doi:10.1007/s11856-011-0094-5 fatcat:dtceg3y6ybbnxmalvlumevcxjy

Anomaly Detection with the Voronoi Diagram Evolutionary Algorithm [article]

Marti Luis, Navarro Laurent
2016 arXiv   pre-print
This paper presents the Voronoi diagram-based evolutionary algorithm (VorEAl). VorEAl partitions input space in abnormal/normal subsets using Voronoi diagrams.  ...  Diagrams are evolved using a multi-objective bio-inspired approach in order to conjointly optimize classification metrics while also being able to represent areas of the data space that are not present  ...  From the union of P t and P off , the best n pop are selected using the non-dominated sorting selection of NSGA-II [3] . This process repeats until the stopping criterion of the algorithm is met.  ... 
arXiv:1610.08640v1 fatcat:43x3ii34wran5j4rjjfpqmy6ue

An approximate method for circle packing and disc covering

Shuangmin Chen, Yuen-Shan Leung, Shiqing Xin, Ying He, Yuanfeng Zhou, Changhe Tu
2018 Communications in Information and Systems  
Using geodesic exponential map, we can compute those centers efficiently on manifold triangle meshes, hereby extending our 2D algorithm to non-Euclidean domains.  ...  to the covering (resp. packing) problem can be obtained by iteratively updating the centers of the circumscribed (resp. inscribed) circles of the Voronoi cells.  ...  This work is partially supported by NSF of China (61772016, 61772312), China 973 Program (2015CB352502) and the key research and development project of Shandong province (2017GGX10110).  ... 
doi:10.4310/cis.2018.v18.n2.a1 fatcat:ratgru6f4zdhljyhithr7ffxey

VorAIS

Luis Martí, Arsene Fansi Tchango, Laurent Navarro, Marc Schoenauer
2016 Proceedings of the 2016 on Genetic and Evolutionary Computation Conference Companion - GECCO '16 Companion  
VorAIS models the self/non-self using a Voronoi diagram that determines which areas of the problem domain correspond to self or to non-self.  ...  This paper introduces the Voronoi diagram-based Artificial Immune System (VorAIS).  ...  From the union of Pt and P off , the best npop are selected using the non-dominated sorting selection of NSGA-II [2] . 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00Hypersphere Self Only Hypersphere  ... 
doi:10.1145/2908961.2909027 dblp:conf/gecco/MartiTNS16 fatcat:5rmyfsn5grfq5mcjuzeayzygwq

Image partitioning into convex polygons

Liuyun Duan, Florent Lafarge
2015 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
The overall strategy consists in building a Voronoi diagram that conforms to preliminarily detected line-segments, before homogenizing the partition by spatial point process distributed over the image  ...  It presents several interesting properties in terms of geometric guarantees, region compactness and scalability.  ...  Finally the algorithmic complexity to build a Voronoi diagram when dim K = 2 is only in O(n log n). Spatial point processes can be used to generate the seeds of a Voronoi diagram.  ... 
doi:10.1109/cvpr.2015.7298931 dblp:conf/cvpr/DuanL15 fatcat:lwh5oo6btba5pifcqopkqvrbxm

Capacity-Constrained Voronoi Diagrams in Continuous Spaces

Michael Balzer
2009 2009 Sixth International Symposium on Voronoi Diagrams  
In this paper, we present two approaches for computing such capacity-constrained Voronoi diagrams in continuous spaces.  ...  Ordinary Voronoi Diagrams We consider a set S = {s 1 , . . . , s n } of n points in the Euclidean plane R 2 , and assume that 2 ≤ n < ∞.  ...  sites arranged in a regular grid (c) non-regularly distributed sites using the ordinary Euclidean distance (d) non-regularly distributed sites using the weighted AW distance Figure 1 . 1 Examples of  ... 
doi:10.1109/isvd.2009.28 dblp:conf/isvd/Balzer09 fatcat:fbpcetm45bgn3p2jwvf4x5rivu

Shortest Paths and Voronoi Diagrams with Transportation Networks Under General Distances [chapter]

Sang Won Bae, Kyung-Yong Chwa
2005 Lecture Notes in Computer Science  
However, this paper first considers distances induced by general distances and transportation networks, and present a unifying approach to compute Voronoi diagrams under such a general setting.  ...  Computing the Voronoi diagrams for non-piercing needles. The abstract Voronoi diagram is a unifying approach to define and compute general Voronoi diagrams, introduced by Klein [11] .  ...  For the Euclidean case, the Voronoi diagram for pairwise non-piercing needles has been shown to be an abstract Voronoi diagram.  ... 
doi:10.1007/11602613_100 fatcat:dfhjyi7pabbadiy7ruszrmyaeu

Distributed Algorithms for Environment Partitioning in Mobile Robotic Networks

Marco Pavone, Alessandro Arsie, Emilio Frazzoli, Francesco Bullo
2011 IEEE Transactions on Automatic Control  
and median Voronoi diagrams.  ...  Our approach is related to the classic Lloyd algorithm, and exploits the unique features of power diagrams.  ...  Bressan's contribution in deriving the proof of Theorem 3.12.  ... 
doi:10.1109/tac.2011.2112410 fatcat:ioyfw5khbnft3podllpbqlgdza

Equitable Partitioning Policies for Mobile Robotic Networks [article]

Marco Pavone, Alessandro Arsie, Emilio Frazzoli, Francesco Bullo
2009 arXiv   pre-print
Our approach is related to the classic Lloyd algorithm, and exploits the unique features of power diagrams.  ...  We also consider the issue of achieving convex and equitable partitions where subregions have shapes similar to those of regular polygons.  ...  It is easy to verify that the only admissible configuration for the boundary points in order Example of non-existence of an equitable Voronoi diagram on a line.  ... 
arXiv:0903.5267v1 fatcat:knh42s5vubgb5nw7ju7hu4w2ju

Intersections with random geometric objects

Prosenjit Bose, Luc Devroye
1998 Computational geometry  
Using this result, we explore the intersection complexity of a random Voronoi diagram with the following target objects which may or may not be random: a line segment, a Voronoi diagram, a minimum spanning  ...  tree, a Gabriel graph, a relative neighborhood graph, a Hamiltonian circuit, a furthest point Voronoi diagram, a convex hull, a k-dimensional tree, and a rectangular grid. ¢ 1998 Elsevier Science B.V.  ...  Adding non-convex hull points does not alter the furthest-point Voronoi diagram. 1 E{N' I CH } <~ ~ × (c]N"+ c2(3N"-6)Av/-n), where N t is the number of intersections between the clipped G and the Voronoi  ... 
doi:10.1016/s0925-7721(98)00004-2 fatcat:fpbk62ycsbbd7ahj6hebtsfscm
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