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The k-Nearest-Neighbor Voronoi Diagram Revisited

Chih-Hung Liu, Evanthia Papadopoulou, Der-Tsai Lee
2013 Algorithmica  
We 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.  ... 
doi:10.1007/s00453-013-9809-9 fatcat:tmvkcztrcvecvcivvx73faqr7a

INSQ: An Influential Neighbor Set Based Moving kNN Query Processing System [article]

Chuanwen Li, Yu Gu, Jianzhong Qi, Ge Yu, Rui Zhang, Qingxu Deng
2021 arXiv   pre-print
We 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] .  ... 
arXiv:1602.00363v3 fatcat:lhicsuievjdolokty6dhpbqz5i

INSQ: An influential neighbor set based moving kNN query processing system

Chuanwen Li, Yu Gu, Jianzhong Qi, Ge Yu, Rui Zhang, Qingxu Deng
2016 2016 IEEE 32nd International Conference on Data Engineering (ICDE)  
We 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] .  ... 
doi:10.1109/icde.2016.7498339 dblp:conf/icde/Li0QYZD16 fatcat:m43uble3ujdjrn3qke4njwomri

Processing movingkNN queries using influential neighbor sets

Chuanwen Li, Yu Gu, Jianzhong Qi, Ge Yu, Rui Zhang, Wang Yi
2014 Proceedings of the VLDB Endowment  
Existing moving 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] .  ... 
doi:10.14778/2735471.2735473 fatcat:4wg6e7xey5hp5k4qkyylar5cey

Hyperbolic Voronoi diagrams made easy [article]

Frank Nielsen, Richard Nock
2009 arXiv   pre-print
Finally, we consider two useful primitives on 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.  ... 
arXiv:0903.3287v1 fatcat:rdjg5l46azcaxkhrj3gbbomqu4

Restricted Power Diagrams on the GPU

J. Basselin, L. Alonso, N. Ray, D. Sokolov, S. Lefebvre, B. Lévy
2021 Computer graphics forum (Print)  
We compute 3D 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].  ... 
doi:10.1111/cgf.142610 fatcat:5dvh4wikcrer5mclgx2pasu2ce

Ultrafast Expected Time Parallel Algorithms

Philip D MacKenzie, Quentin F Stout
1998 Journal of Algorithms  
Reif and Sen [32] have recently given PT-optimal n processor, Θ(log n) expected time randomized algorithms for constructing 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  ... 
doi:10.1006/jagm.1997.0892 fatcat:azwytbtcpnd53ndkcgrgumz55i

UV-diagram: a voronoi diagram for uncertain spatial databases

Xike Xie, Reynold Cheng, Man Lung Yiu, Liwen Sun, Jinchuan Chen
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.  ... 
doi:10.1007/s00778-012-0290-x fatcat:taoghck7hnb6rjs3lmg4gw6tyq

On 2-Site Voronoi Diagrams under Geometric Distance Functions

Gill Barequet, Matthew T. Dickerson, David Eppstein, David Hodorkovsky, Kira Vyatkina
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 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  ... 
doi:10.1109/isvd.2011.13 dblp:conf/isvd/BarequetDEHV11 fatcat:mvrsplp6s5e5jbnwhhc2ckqrda

On 2-Site Voronoi Diagrams Under Geometric Distance Functions

Gill Barequet, Matthew Dickerson, David Eppstein, David Hodorkovsky, Kira Vyatkina
2013 Journal of Computer Science and Technology  
We consider a few more such distance functions, based on geometric primitives, and analyze 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  ... 
doi:10.1007/s11390-013-1328-2 fatcat:6o456u3ipnbavdtxvrozed6d2e

An Output-Sensitive Approach for the L 1/L ∞ k-Nearest-Neighbor Voronoi Diagram [chapter]

Chih-Hung Liu, Evanthia Papadopoulou, D. T. Lee
2011 Lecture Notes in Computer Science  
This paper 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.  ... 
doi:10.1007/978-3-642-23719-5_7 fatcat:yijwtk7tcngtbek77sjt7k2ot4

An optimal algorithm for computing the minimum vertex distance between two crossing convex polygons

G. T. Toussaint
1984 Computing  
An optimal O(m+n) algorithm is presented for computing 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.  ... 
doi:10.1007/bf02243778 fatcat:5ubynf3oxrh5ven6b37jurbijm

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.  ... 
doi:10.1007/978-3-319-17885-1_101469 fatcat:rnvtcucz6vfulmc6voflfymen4

Secure nearest neighbor revisited

Bin Yao, Feifei Li, Xiaokui Xiao
2013 2013 IEEE 29th International Conference on Data Engineering (ICDE)  
In this paper, we investigate 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.  ... 
doi:10.1109/icde.2013.6544870 dblp:conf/icde/0002LX13 fatcat:s7b32m37grhhhnjot5cef4hstm

Approximate Nearest Neighbor Queries Revisited

T. M. Chan
1998 Discrete & Computational Geometry  
This paper proposes new methods to answer approximate 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 .  ... 
doi:10.1007/pl00009390 fatcat:sguewsrtgra77lbjy3jiqupxpi
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