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Nearest neighbors search using point location in balls with applications to approximate Voronoi decompositions

2006
*
Journal of computer and system sciences (Print)
*

We present alternate reductions of the

doi:10.1016/j.jcss.2006.01.007
fatcat:vek47pgeezg63jdjkx76y5z7jm
*nearest**neighbor**searching*problem*to**Point**Location**in**Balls*that reduces the space bound of Sariel Har-Peled's [S. ... We further reduce the number of*balls*by a new hierarchical*decomposition*scheme and a generalization of PLEBs*to*achieve linear space*decomposition*for*nearest**neighbor**searching*. ... One of the most fundamental problems*with*diverse*applications*is*to*build a data structure on P that supports*nearest**neighbor**searching*efficiently. ...##
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Down the Rabbit Hole: Robust Proximity Search and Density Estimation in Sublinear Space
[article]

2013
*
arXiv
*
pre-print

Our approach generalizes

arXiv:1111.2942v3
fatcat:4moay5csffgc5mvifsuxsyg7u4
*to*other distance based estimation of densities of similar flavor. We also study the problem of*approximating*some of these quantities when*using*sampling. ... sum of squared distances of k closest*points**to*the query*point*. ... The authors thank Pankaj Agarwal and Kasturi Varadarajan for*useful*discussions on the problems studied*in*this paper. ...##
###
Page 9214 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

2004k:68170
2004k:68170 68U05 Sabharwal, Yogish (6-IITD-CS; Delhi) ; Sharma, Nishant (6-IITD-CS; Delhi) ; Sen, Sandeep (6-IITD-CS; Delhi)

*Nearest**neighbors**search**using**point**location**in**balls**with**applications*... Summary: “We present improved reductions of the*nearest*neigh- bor*searching*problem*to**point**location**in**balls*by constructing linear size*approximate**Voronoi*diagrams while maintaining the logarithmic ...##
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ANN queries: covering Voronoi diagram with hyperboxes
[article]

2014
*
arXiv
*
pre-print

*nearest*

*neighbors*(ANNs)

*to*a given query

*point*q ∈ X. ... The following are the characteristics of

*points*belonging

*to*set S': - ∀ s ∈ S', ∃ a

*point*p ∈ X such that |pq| <ϵ and the

*nearest*

*neighbor*of p is s, and - ∃ a s' ∈ S' such that s' is a

*nearest*

*neighbor*... The cost

*in*associating sites

*to*main box tree leaves involve dn

*point*

*location*

*searches*per each level of the main box tree. The same is

*applicable*

*to*auxiliary box trees. ...

##
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Down the Rabbit Hole: Robust Proximity Search and Density Estimation in Sublinear Space

2012
*
2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
*

Our approach generalizes

doi:10.1109/focs.2012.31
dblp:conf/focs/Har-PeledK12
fatcat:qevvq5mbojf3pjnjnvfdbfiu3y
*to*other distance based estimation of densities of similar flavor. We also study the problem of*approximating*some of these quantities when*using*sampling. ...*Using*this, we provide a sublinear space data-structure that can estimate the density of a*point*set under various measures, including: (i) sum of distances of k closest*points**to*the query*point*, and ... The authors thank Pankaj Agarwal and Kasturi Varadarajan for*useful*discussions on the problems studied*in*this paper. ...##
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A Fast Algorithm for Well-Spaced Points and Approximate Delaunay Graphs
[article]

2013
*
arXiv
*
pre-print

*To*gain this new efficiency, the algorithm

*approximately*maintains the

*Voronoi*diagram of the current set of

*points*by storing a superset of the Delaunay

*neighbors*of each

*point*. ... We present a new algorithm that produces a well-spaced superset of

*points*conforming

*to*a given input set

*in*any dimension

*with*guaranteed optimal output size. ... It also introduces a new walk-based

*point*

*location*method that can

*locate*the

*nearest*

*neighbor*of a

*point*

*to*be inserted

*in*constant time after 2 O(d) n log n time for preprocessing. ...

##
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Conic nearest neighbor queries and approximate Voronoi diagrams

2015
*
Computational geometry
*

Given a cone C and a set S of n

doi:10.1016/j.comgeo.2014.08.002
fatcat:wbsb4cehl5ffbmysl5srlp4rge
*points**in*R d , we want*to*preprocess S into a data structure so that we can find fast an*approximate**nearest**neighbor**to*a query*point*q*with*respect*to*the*points*of S ... We develop an*approximate*conic*Voronoi*diagram of O(n/ε d ) size that supports conic*nearest**neighbor*queries*in*O(log(n/ε)) time. ... We thank the anonymous referees for suggesting a generalization of our result and numerous ways*to*improve its presentation. ...##
###
A fast algorithm for well-spaced points and approximate delaunay graphs

2013
*
Proceedings of the 29th annual symposium on Symposuim on computational geometry - SoCG '13
*

*To*gain this new e ciency, the algorithm

*approximately*maintains the

*Voronoi*diagram of the current set of

*points*by storing a superset of the Delaunay

*neighbors*of each

*point*. ... We present a new algorithm that produces a well-spaced superset of

*points*conforming

*to*a given input set

*in*any dimension

*with*guaranteed optimal output size. ... It also introduces a new walk-based

*point*

*location*method that can

*locate*the

*nearest*

*neighbor*of a

*point*

*to*be inserted

*in*constant time after 2 O(d) n log n time for preprocessing. ...

##
###
A fast algorithm for well-spaced points and approximate delaunay graphs

2013
*
Proceedings of the 29th annual symposium on Symposuim on computational geometry - SoCG '13
*

*To*gain this new e ciency, the algorithm

*approximately*maintains the

*Voronoi*diagram of the current set of

*points*by storing a superset of the Delaunay

*neighbors*of each

*point*. ... We present a new algorithm that produces a well-spaced superset of

*points*conforming

*to*a given input set

*in*any dimension

*with*guaranteed optimal output size. ... It also introduces a new walk-based

*point*

*location*method that can

*locate*the

*nearest*

*neighbor*of a

*point*

*to*be inserted

*in*constant time after 2 O(d) n log n time for preprocessing. ...

##
###
Restricting Voronoi diagrams to meshes using corner validation

2017
*
Computer graphics forum (Print)
*

Restricted

doi:10.1111/cgf.13247
fatcat:go7lzqxrdzclticrdiov37ps54
*Voronoi*diagrams are a fundamental geometric structure*used**in*many*applications*such as surface reconstruction from*point*sets or optimal transport. ...*In*this paper, we extend Lévy and Bonneel's approach [LB12] based on*nearest**neighbor*queries. We show that their method is limited when the sites are not*located*on X. ... Introduction*Voronoi*diagrams are fundamental tools*used**in*many*applications*. A*Voronoi*diagram is a*decomposition*of space induced by a finite set of*points*called sites. ...##
###
Approximating Minimization Diagrams and Generalized Proximity Search

2013
*
2013 IEEE 54th Annual Symposium on Foundations of Computer Science
*

*Applications*include

*approximating*the

*Voronoi*diagram of (additively or multiplicatively) weighted

*points*. ... Our technique also works for more general distance functions, such as metrics induced by convex bodies, and the

*nearest*furthest-

*neighbor*distance

*to*a set of

*point*sets. ...

*Approximate*

*nearest*

*neighbor*.

*In*typical

*applications*, however, it is usually sufficient

*to*return an

*approximate*

*nearest*

*neighbor*(ANN). ...

##
###
Group Enclosing Queries

2011
*
IEEE Transactions on Knowledge and Data Engineering
*

Index Terms-Aggregate

doi:10.1109/tkde.2010.181
fatcat:fo5cfv3i4ndqfmklhlyfxcpm4u
*nearest**neighbor*,*approximate**nearest**neighbor*, minmax*nearest**neighbor*,*nearest**neighbor*3 ... Our main*approximation*algorithm has a worst case √ 2-*approximation*ratio if one can find the exact*nearest**neighbor*of a*point*. ... For line 2*in*Algorithm 2, one could*use*a BBDtree*with*optimal*approximate**nearest**neighbor**search**to*find a (1 + ǫ)-*approximate**nearest**neighbor*from P for c*in*O(log N ) query cost [5] as we have ...##
###
Meshless voronoi on the GPU

2018
*
ACM Transactions on Graphics
*

*To*ease the reproducibility of our results, the full documented source code is included

*in*the supplemental material. ... We

*search*them

*in*the k

*nearest*

*neighbors*of the seed. ... Thus, by exploiting the specific spatial distribution of the

*point*-sets

*used*

*in*this type of

*applications*, our algorithm computes each cell independently,

*in*parallel, based on its

*nearest*

*neighbors*. ...

##
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Approximate Nearest Neighbor: Towards Removing the Curse of Dimensionality

2012
*
Theory of Computing
*

We present two algorithms for the

doi:10.4086/toc.2012.v008a014
dblp:journals/toc/Har-PeledIM12
fatcat:g2jrsdozzrfytcae5phpwwoksu
*approximate**nearest**neighbor*problem*in*high-dimensional spaces. ... We also show*applications**to*other high-dimensional geometric problems, such as the*approximate*minimum spanning tree. ... Acknowledgments The authors would like*to*thank Alexandr Andoni, Jelani Nelson, Steve Oudot, Ashish Goel and the referees for their very helpful comments on this paper. ...##
###
Approximating Minimization Diagrams and Generalized Proximity Search
[article]

2013
*
arXiv
*
pre-print

*Applications*include

*approximating*the

*Voronoi*diagram of (additively or multiplicatively) weighted

*points*. ... Our technique also works for more general distance functions, such as metrics induced by convex bodies, and the

*nearest*furthest-

*neighbor*distance

*to*a set of

*point*sets. ...

*Approximate*

*nearest*

*neighbor*.

*In*typical

*applications*, however, it is usually sufficient

*to*return an

*approximate*

*nearest*

*neighbor*(ANN). ...

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