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The k-Nearest-Neighbor Voronoi Diagram Revisited

2013
*
Algorithmica
*

We

doi:10.1007/s00453-013-9809-9
fatcat:tmvkcztrcvecvcivvx73faqr7a
*revisit**the**k*-*nearest*-*neighbor*(*k*-NN)*Voronoi**diagram*and present a new paradigm for its construction. ... We introduce*the**k*-NN Delaunay graph, which is*the*graph-theoretic dual of*the**k*-NN*Voronoi**diagram*, and use it as a base to directly compute this*diagram*in R 2 . ... In this paper, we*revisit**the**k*-NN*Voronoi**diagram*and propose an output-sensitive approach to compute*the*L ∞ (equiv. L 1 )*k*-NN*Voronoi**diagram*. ...##
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INSQ: An Influential Neighbor Set Based Moving kNN Query Processing System
[article]

2021
*
arXiv
*
pre-print

We

arXiv:1602.00363v3
fatcat:lhicsuievjdolokty6dhpbqz5i
*revisit**the*moving*k**nearest**neighbor*(MkNN) query, which computes one's*k**nearest**neighbor*set and maintains it while at move. ... As long as*the**the*current*k**nearest**neighbors*are closer to*the*query object than*the*safe guarding objects are,*the*current*k**nearest**neighbors*stay valid and no recomputation is required. ... In this paper we*revisit*a major type of moving query,*the*moving*k**nearest**neighbor*(MkNN) query [1] , [4] . ...##
###
INSQ: An influential neighbor set based moving kNN query processing system

2016
*
2016 IEEE 32nd International Conference on Data Engineering (ICDE)
*

We

doi:10.1109/icde.2016.7498339
dblp:conf/icde/Li0QYZD16
fatcat:m43uble3ujdjrn3qke4njwomri
*revisit**the*moving*k**nearest**neighbor*(MkNN) query, which computes one's*k**nearest**neighbor*set and maintains it while at move. ... As long as*the**the*current*k**nearest**neighbors*are closer to*the*query object than*the*safe guarding objects are,*the*current*k**nearest**neighbors*stay valid and no recomputation is required. ... In this paper we*revisit*a major type of moving query,*the*moving*k**nearest**neighbor*(MkNN) query [1] , [4] . ...##
###
Processing movingkNN queries using influential neighbor sets

2014
*
Proceedings of the VLDB Endowment
*

Existing moving

doi:10.14778/2735471.2735473
fatcat:4wg6e7xey5hp5k4qkyylar5cey
*k**nearest**neighbor*algorithms lack efficiency due to either computing small safe regions and have to recompute frequently or computing large safe regions (i.e., an order-*k**Voronoi*cell) ... We prove that, as long as*the**the*current*k**nearest**neighbors*are closer to*the*query object than*the*safe guarding objects,*the*current*k**nearest**neighbors*stay valid and no recomputation is required. ... In this paper we*revisit*a major type of moving query,*the*moving*k**nearest**neighbor*(MkNN) query [4, 16, 21, 23] . ...##
###
Hyperbolic Voronoi diagrams made easy
[article]

2009
*
arXiv
*
pre-print

Finally, we consider two useful primitives on

arXiv:0903.3287v1
fatcat:rdjg5l46azcaxkhrj3gbbomqu4
*the*hyperbolic*Voronoi**diagrams*for designing tailored user interfaces of an image catalog browsing application in*the*hyperbolic disk: (1) finding*nearest*... We present a simple framework to compute hyperbolic*Voronoi**diagrams*of finite point sets as affine*diagrams*. ... We thank Cyprien Pindat for implementing in Java an earlier version of*the*image browser application in*the*Poincaré disk model. ...##
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Restricted Power Diagrams on the GPU

2021
*
Computer graphics forum (Print)
*

We compute 3D

doi:10.1111/cgf.142610
fatcat:5dvh4wikcrer5mclgx2pasu2ce
*Voronoi**diagrams*of 10 million points restricted to a mesh in 300 ms on*the*GPU (Nvidia V100). ...*k*-NN query To compute a*Voronoi*cell of a given seed S, we need to find its*k**nearest**neighbors*. ...*The*rest of*the*paper is organized as follows: first we*revisit**the**nearest**neighbors*query ( §2.1) and*Voronoi*cell computation ( §2.2) as done in [RSLL18]. ...##
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Ultrafast Expected Time Parallel Algorithms

1998
*
Journal of Algorithms
*

Reif and Sen [32] have recently given PT-optimal n processor, Θ(log n) expected time randomized algorithms for constructing

doi:10.1006/jagm.1997.0892
fatcat:azwytbtcpnd53ndkcgrgumz55i
*the**Voronoi**Diagram*and finding All*Nearest**Neighbors*. ... Bentley, Weide, and Yao [7] exhibit linear expected time algorithms for All*Nearest**Neighbors*and*Voronoi**Diagram*, and linear expected time Delaunay Triangulation and Largest Empty Circle algorithms follow ...*Voronoi**Diagram*An algorithm similar to*the*one for All*Nearest**Neighbors*will find*the**Voronoi**Diagram*in*the*unit square in constant expected time, and*the*Outer*Voronoi**Diagram*can be found in constant ...##
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UV-diagram: a voronoi diagram for uncertain spatial databases

2012
*
The VLDB journal
*

*The*

*Voronoi*

*diagram*is an important technique for answering

*nearest*-

*neighbor*queries for spatial databases. ...

*The*UV-

*diagram*enables queries that return objects with nonzero chances of being

*the*

*nearest*

*neighbor*(NN) of a given point q. ... We would like to thank

*the*anonymous reviewers for their insightful comments. ...

##
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On 2-Site Voronoi Diagrams under Geometric Distance Functions

2011
*
2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering
*

We consider a few more such distance functions, based on geometric primitives, namely, circles and triangles, and analyze

doi:10.1109/isvd.2011.13
dblp:conf/isvd/BarequetDEHV11
fatcat:mvrsplp6s5e5jbnwhhc2ckqrda
*the*structure and complexity of*the**nearest*-and furthest-*neighbor*2-site*Voronoi*... We*revisit*a new type of*Voronoi**diagram*, in which distance is measured from a point to a pair of points. ... Gill Barequet et al.: 2-Site*Voronoi**Diagrams*...##
###
On 2-Site Voronoi Diagrams Under Geometric Distance Functions

2013
*
Journal of Computer Science and Technology
*

We consider a few more such distance functions, based on geometric primitives, and analyze

doi:10.1007/s11390-013-1328-2
fatcat:6o456u3ipnbavdtxvrozed6d2e
*the*structure and complexity of*the**nearest*- and furthest-*neighbor**Voronoi**diagrams*of a point set with respect ... We*revisit*a new type of a*Voronoi**diagram*, in which distance is measured from a point to a pair of points. ... Gill Barequet et al.: 2-Site*Voronoi**Diagrams*...##
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An Output-Sensitive Approach for the L 1/L ∞ k-Nearest-Neighbor Voronoi Diagram
[chapter]

2011
*
Lecture Notes in Computer Science
*

This paper

doi:10.1007/978-3-642-23719-5_7
fatcat:yijwtk7tcngtbek77sjt7k2ot4
*revisits**the**k*-*nearest*-*neighbor*(*k*-NN)*Voronoi**diagram*and presents*the*first output-sensitive paradigm for its construction. ... In R 2 ,*the*boundary between two*neighboring**k*-NN*Voronoi*regions is a*k*-NN*Voronoi*edge, and*the*intersection point among more than two*neighboring**k*-NN*Voronoi*⋆ regions is a*k*-NN*Voronoi*vertex. ... In this paper, we*revisit**the**k*-NN*Voronoi**diagram*and propose*the*first direct output-sensitive approach to compute*the*L ∞ (equiv. L 1 )*k*-NN*Voronoi**diagram*. ...##
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An optimal algorithm for computing the minimum vertex distance between two crossing convex polygons

1984
*
Computing
*

An optimal O(m+n) algorithm is presented for computing

doi:10.1007/bf02243778
fatcat:5ubynf3oxrh5ven6b37jurbijm
*the*minimum euclidean distance between a vertex p i in P and a vertex q j in Q. ...*The*property used in [7] is*the*fact that for any vertex p i its*nearest**neighbor*p j is adjacent to p i , i.e., it is either p i+1 or p i-1 . ... Therefore, in this region*the**Voronoi**diagram*can be constructed in O(n) time. ...##
###
Visualization Tool
[chapter]

2017
*
Encyclopedia of GIS
*

*diagrams*to process

*k*

*Nearest*

*Neighbor*(kNN) queries. ... Now, to find

*the*

*k*

*nearest*-

*neighbors*of a query object q, VN 3 first finds

*the*first

*nearest*

*neighbor*by simply locating

*the*

*Voronoi*cell that contains q. ...

*The*Additively Weighted (AW-) network

*Voronoi*

*diagram*of S partitions N into regions. ...

##
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Secure nearest neighbor revisited

2013
*
2013 IEEE 29th International Conference on Data Engineering (ICDE)
*

In this paper, we investigate

doi:10.1109/icde.2013.6544870
dblp:conf/icde/0002LX13
fatcat:s7b32m37grhhhnjot5cef4hstm
*the*secure*nearest**neighbor*(SNN) problem, in which a client issues an encrypted query point E(q) to a cloud service provider and asks for an encrypted data point in E(D) ... Since it is impossible to construct secure OPE schemes in standard security models [6], [5], our results imply that one cannot expect to find*the*exact (encrypted)*nearest**neighbor*based on only E(q) and ... CONCLUSION This work*revisits**the*secure*nearest**neighbor*problem. We show*the*insecurity of existing solutions, and*the*hardness of*the*SNN problem. ...##
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Approximate Nearest Neighbor Queries Revisited

1998
*
Discrete & Computational Geometry
*

This paper proposes new methods to answer approximate

doi:10.1007/pl00009390
fatcat:sguewsrtgra77lbjy3jiqupxpi
*nearest**neighbor*queries on a set of n points in d-dimensional Euclidean space. ... any fixed constant d, a data structure with O(ε (1−d)/2 n log n) preprocessing time and O(ε (1−d)/2 log n) query time achieves an approximation factor 1 + ε for any given 0 < ε < 1; a variant reduces*the*... s method This site s can be found by performing*k*= O(log n) point location queries on*the**Voronoi**diagrams*at nodes v 1 , . . . , v*k*. ...
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