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Computation of Spatial Skyline Points
[article]

2019
*
arXiv
*
pre-print

We reduce this problem

arXiv:0909.0814v2
fatcat:g4eg4ccre5fmlksxpg4qenur2a
*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. ...##
###
Voronoi diagrams for polygon-offset distance functions
[chapter]

1997
*
Lecture Notes in Computer Science
*

In this paper we develop the concept

doi:10.1007/3-540-63307-3_60
fatcat:y5loxmfovvgxfbrlxe5yhbs2jy
*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. ...##
###
Anomaly Detection with the Voronoi Diagram Evolutionary Algorithm
[chapter]

2016
*
Lecture Notes in Computer Science
*

From the union

doi:10.1007/978-3-319-45823-6_65
fatcat:oxyten7qejaafapgljfk5zffq4
*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 ...##
###
Compact Voronoi Diagrams for Moving Convex Polygons
[chapter]

2000
*
Lecture Notes in Computer Science
*

We

doi:10.1007/3-540-44985-x_30
fatcat:bb63fodayja6xipo7jclv7ylhm
*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*. ...##
###
Voronoi Diagram for Convex Polygonal Sites with Convex Polygon-Offset Distance Function
[chapter]

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. ...

##
###
Zone diagrams in compact subsets of uniformly convex normed spaces

2011
*
Israel Journal of Mathematics
*

A zone

doi:10.1007/s11856-011-0094-5
fatcat:dtceg3y6ybbnxmalvlumevcxjy
*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 ...##
###
Anomaly Detection with the Voronoi Diagram Evolutionary Algorithm
[article]

2016
*
arXiv
*
pre-print

This paper presents the

arXiv:1610.08640v1
fatcat:43x3ii34wran5j4rjjfpqmy6ue
*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. ...##
###
An approximate method for circle packing and disc covering

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). ...

##
###
VorAIS

2016
*
Proceedings of the 2016 on Genetic and Evolutionary Computation Conference Companion - GECCO '16 Companion
*

VorAIS models the self/

doi:10.1145/2908961.2909027
dblp:conf/gecco/MartiTNS16
fatcat:5rmyfsn5grfq5mcjuzeayzygwq
*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 ...##
###
Image partitioning into convex polygons

2015
*
2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
*

The overall strategy consists in building a

doi:10.1109/cvpr.2015.7298931
dblp:conf/cvpr/DuanL15
fatcat:lwh5oo6btba5pifcqopkqvrbxm
*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*. ...##
###
Capacity-Constrained Voronoi Diagrams in Continuous Spaces

2009
*
2009 Sixth International Symposium on Voronoi Diagrams
*

In this paper, we present two approaches for

doi:10.1109/isvd.2009.28
dblp:conf/isvd/Balzer09
fatcat:fbpcetm45bgn3p2jwvf4x5rivu
*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*...##
###
Shortest Paths and Voronoi Diagrams with Transportation Networks Under General Distances
[chapter]

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

doi:10.1007/11602613_100
fatcat:dfhjyi7pabbadiy7ruszrmyaeu
*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*. ...##
###
Distributed Algorithms for Environment Partitioning in Mobile Robotic Networks

2011
*
IEEE Transactions on Automatic Control
*

and median

doi:10.1109/tac.2011.2112410
fatcat:ioyfw5khbnft3podllpbqlgdza
*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. ...##
###
Equitable Partitioning Policies for Mobile Robotic Networks
[article]

2009
*
arXiv
*
pre-print

Our approach is related to the classic Lloyd algorithm, and exploits the unique features

arXiv:0903.5267v1
fatcat:knh42s5vubgb5nw7ju7hu4w2ju
*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. ...##
###
Intersections with random geometric objects

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*...

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