Filters








490 Hits in 5.9 sec

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

Yogish Sabharwal, Nishant Sharma, Sandeep Sen
2006 Journal of computer and system sciences (Print)  
We present alternate reductions of the 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.  ... 
doi:10.1016/j.jcss.2006.01.007 fatcat:vek47pgeezg63jdjkx76y5z7jm

Down the Rabbit Hole: Robust Proximity Search and Density Estimation in Sublinear Space [article]

Sariel Har-Peled, Nirman Kumar
2013 arXiv   pre-print
Our approach generalizes 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.  ... 
arXiv:1111.2942v3 fatcat:4moay5csffgc5mvifsuxsyg7u4

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  ... 

ANN queries: covering Voronoi diagram with hyperboxes [article]

Rajasekhar Inkulu, Sanjiv Kapoor
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.  ... 
arXiv:1111.5893v2 fatcat:ynqegt3bjjfjdfturz7quhlcji

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

Sariel Har-Peled, Nirman Kumar
2012 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science  
Our approach generalizes 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.  ... 
doi:10.1109/focs.2012.31 dblp:conf/focs/Har-PeledK12 fatcat:qevvq5mbojf3pjnjnvfdbfiu3y

A Fast Algorithm for Well-Spaced Points and Approximate Delaunay Graphs [article]

Gary L. Miller, Donald R. Sheehy, Ameya Velingker
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.  ... 
arXiv:1304.0524v1 fatcat:fwyvoncnw5hjtg626a2twrflyi

Conic nearest neighbor queries and approximate Voronoi diagrams

Stefan Funke, Theocharis Malamatos, Domagoj Matijevic, Nicola Wolpert
2015 Computational geometry  
Given a cone C and a set S of n 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.  ... 
doi:10.1016/j.comgeo.2014.08.002 fatcat:wbsb4cehl5ffbmysl5srlp4rge

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

Gary L. Miller, Donald R. Sheehy, Ameya Velingker
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.  ... 
doi:10.1145/2493132.2462404 fatcat:dwxs2lxp2jfxph52xd375n4xgm

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

Gary L. Miller, Donald R. Sheehy, Ameya Velingker
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.  ... 
doi:10.1145/2462356.2462404 dblp:conf/compgeom/MillerSV13 fatcat:r2kcpc4zp5hu3fymtjt3ibhnnu

Restricting Voronoi diagrams to meshes using corner validation

M. Sainlot, V. Nivoliers, D. Attali
2017 Computer graphics forum (Print)  
Restricted 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.  ... 
doi:10.1111/cgf.13247 fatcat:go7lzqxrdzclticrdiov37ps54

Approximating Minimization Diagrams and Generalized Proximity Search

Sariel Har-Peled, Nirman Kumar
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).  ... 
doi:10.1109/focs.2013.82 dblp:conf/focs/Har-PeledK13 fatcat:afpremzkljf4lhz2b3ldmjlstq

Group Enclosing Queries

Feifei Li, Bin Yao, Piyush Kumar
2011 IEEE Transactions on Knowledge and Data Engineering  
Index Terms-Aggregate 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  ... 
doi:10.1109/tkde.2010.181 fatcat:fo5cfv3i4ndqfmklhlyfxcpm4u

Meshless voronoi on the GPU

Nicolas Ray, Dmitry Sokolov, Sylvain Lefebvre, Bruno Lévy
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.  ... 
doi:10.1145/3272127.3275092 fatcat:3cwj5r7355bojbcfj27kb6hkfu

Approximate Nearest Neighbor: Towards Removing the Curse of Dimensionality

Sariel Har-Peled, Piotr Indyk, Rajeev Motwani
2012 Theory of Computing  
We present two algorithms for the 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.  ... 
doi:10.4086/toc.2012.v008a014 dblp:journals/toc/Har-PeledIM12 fatcat:g2jrsdozzrfytcae5phpwwoksu

Approximating Minimization Diagrams and Generalized Proximity Search [article]

Sariel Har-Peled, Nirman Kumar
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).  ... 
arXiv:1304.0393v2 fatcat:ykp3xqg7z5fbdnkgs5uquorv64
« Previous Showing results 1 — 15 out of 490 results