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Facility location problems in the plane based on reverse nearest neighbor queries

S. Cabello, J.M. Díaz-Báñez, S. Langerman, C. Seara, I. Ventura
2010 European Journal of Operational Research  
In this paper, we introduce and investigate new optimization problems in the plane according to the Bichromatic Reverse Nearest Neighbor (BRNN) query.  ...  The Reverse Nearest Neighbor (RNN) problem is to find all points in a given data set whose nearest neighbor is a given query point.  ...  The authors would like to thank the Ayuntamiento de Almonte for their support and the other workshop participants for helpful comments.  ... 
doi:10.1016/j.ejor.2009.04.021 fatcat:6qsoz7fi4ne67lscgnsu5fltjm

Reverse top-k queries

Akrivi Vlachou, Christos Doulkeridis, Yannis Kotidis, Kjetil Norvag
2010 2010 IEEE 26th International Conference on Data Engineering (ICDE 2010)  
We formally define reverse top-k queries and introduce two versions of the query, namely monochromatic and bichromatic.  ...  Then, we study in more details the case of bichromatic reverse topk query, which is more interesting for practical applications.  ...  Vlachou and C. Doulkeridis. Y. Kotidis was supported by the Basic Research Funding Program 2008 of AUEB.  ... 
doi:10.1109/icde.2010.5447890 dblp:conf/icde/VlachouDKN10 fatcat:6fk6wpcdkzbkzcarpnujey6ehu

External Memory Computational Geometry Revisited [chapter]

Christian Breimann, Jan Vahrenhold
2003 Lecture Notes in Computer Science  
Neighbor 16 Polygon Triangulation 6 All Nearest Neighbors 17 Vertical Ray-Shooting 7 Reverse Nearest Neighbors 18 Planar Point Location 8 K-Nearest Neighbors 19 Bichromatic Segment Intersec- tion  ...  ), where for each point p ∈ S, we wish to determine its nearest neighbor in S \ {p} (see Problem 6.5).  ... 
doi:10.1007/3-540-36574-5_6 fatcat:epyks4upofgf3i4tm2pit3rgwi

Efficiently Processing Continuous k-NN Queries on Data Streams

Christian Bohm, Beng Chin Ooi, Claudia Plant, Ying Yan
2007 2007 IEEE 23rd International Conference on Data Engineering  
Our method is based on three ideas, (1) selecting exactly those objects from the stream which are able to become the nearest neighbor of one or more continuous queries and storing them in a skyline data  ...  Efficiently processing continuous k-nearest neighbor queries on data streams is important in many application domains, e. g. for network intrusion detection or in querysubscriber systems.  ...  More exactly, the object o searches for the bichromatic reverse nearest neighbor among the queries, as defined, e.g. in [12] .  ... 
doi:10.1109/icde.2007.367861 dblp:conf/icde/BohmOPY07 fatcat:5ubuuhmyg5gyrhyj7dbtwvv6ne

Reverse k-ranks query

Zhao Zhang, Cheqing Jin, Qiangqiang Kang
2014 Proceedings of the VLDB Endowment  
Hence, we propose three novel approaches to efficiently process R-kRanks query, including one tree-based method and two batch-pruning-based methods.  ...  Finding matching customers for a given product based on individual user's preference is critical for many applications, especially in e-commerce.  ...  Vlachou et al. proposed one solution for monochromatic reverse top-k query and two solutions for bichromatic reverse top-k query, namely RTA and GRTA [21] .  ... 
doi:10.14778/2732951.2732952 fatcat:dbwfecsvkrddfn6zqruuid5aue

Efficient reverse k-nearest neighbor search in arbitrary metric spaces

Elke Achtert, Christian Böhm, Peer Kröger, Peter Kunath, Alexey Pryakhin, Matthias Renz
2006 Proceedings of the 2006 ACM SIGMOD international conference on Management of data - SIGMOD '06  
In particular, we approximate the k-nearest neighbor distance for each data object by upper and lower bounds using two functions of only two parameters each.  ...  The reverse k-nearest neighbor (RkNN) problem, i.e. finding all objects in a data set the k-nearest neighbors of which include a specified query object, is a generalization of the reverse 1-nearest neighbor  ...  Acknowledgement We are grateful with Yufei Tao, Dimitris Papadias, Xiang Lian and Xiaokui Xiao providing us the source code of their Reverse kNN Search in [11] .  ... 
doi:10.1145/1142473.1142531 dblp:conf/sigmod/AchtertBKKPR06 fatcat:3qgpvzngvrbf3gxvofqb26vxge

On efficiently finding reverse k-nearest neighbors over uncertain graphs

Yunjun Gao, Xiaoye Miao, Gang Chen, Baihua Zheng, Deng Cai, Huiyong Cui
2017 The VLDB journal  
In this paper, we systematically study the problem of reverse k-nearest neighbor search on uncertain graphs (UG-RkNN search for short), where graph edges contain uncertainty.  ...  Reverse k-nearest neighbor (RkNN) query on graphs returns the data objects that take a specified query object q as one of their k-nearest neighbors.  ...  There are four main research lines on uncertain graphs: (i) the queries based on shortest path distances over uncertain graphs, such as k-nearest neighbor search on uncertain graphs [36] , aggregate nearest  ... 
doi:10.1007/s00778-017-0460-y fatcat:tachc5xhorhdvgaxgsxnh2edbe

Finding Relevant Points for Nearest-Neighbor Classification [article]

David Eppstein
2021 arXiv   pre-print
In nearest-neighbor classification problems, a set of d-dimensional training points are given, each with a known classification, and are used to infer unknown classifications of other points by using the  ...  The time bounds for our algorithm, in any constant dimension d≥ 3, improve on a previous algorithm for the same problem by Clarkson (FOCS 1994).  ...  Three of those neighbors were already identified as relevant from the minimum spanning tree; the other two neighbors, identified as relevant in the second part of the algorithm, are highlighted. • Using  ... 
arXiv:2110.06163v1 fatcat:gwp56fg2fbd4zpaug3dldetlje

Spanning Trees and Spanners [chapter]

David Eppstein
2000 Handbook of Computational Geometry  
We survey results in geometric network design theory, including algorithms for constructing minimum spanning trees and low-dilation graphs.  ...  nearest neighbor pair of P and Q.  ...  [2] found a more efficient method for high dimensional minimum spanning trees, via bichromatic nearest neighbors.  ... 
doi:10.1016/b978-044482537-7/50010-3 fatcat:gitonpgfozgfribivszd6gf5cy

On multi-type reverse nearest neighbor search

Xiaobin Ma, Chengyang Zhang, Shashi Shekhar, Yan Huang, Hui Xiong
2011 Data & Knowledge Engineering  
Traditionally, a reverse nearest neighbor (RNN) query finds all the objects that have the query point as their nearest neighbor.  ...  This paper presents a study of the Multi-Type Reverse Nearest Neighbor (MTRNN) query problem.  ...  [23] formalized a maximum bichromatic reverse nearest neighbor (MaxBRNN) problem that finds an optimal region maximizing the size of BRNNs.  ... 
doi:10.1016/j.datak.2011.06.003 fatcat:6bfh3dxpujgpdnrn2dtriawu54

Reverse Nearest Neighbor Heat Maps: A Tool for Influence Exploration [article]

Yu Sun, Rui Zhang, Andy Yuan Xue, Jianzhong Qi, Xiaoyong Du
2016 arXiv   pre-print
We study the problem of constructing a reverse nearest neighbor (RNN) heat map by finding the RNN set of every point in a two-dimensional space.  ...  The heat map provides a global view on the influence distribution in the space, and hence supports exploratory analyses in many applications such as marketing and resource management.  ...  For instance, Lu et al. [13] investigate reverse spatial and textual nearest neighbor queries, in which both location and textual descriptions are considered in the distance metric.  ... 
arXiv:1602.00389v2 fatcat:xhoae7qvwbfedc55m3rig3j6f4

On efficient mutual nearest neighbor query processing in spatial databases

Yunjun Gao, Baihua Zheng, Gencai Chen, Qing Li
2009 Data & Knowledge Engineering  
This paper studies a new form of nearest neighbor queries in spatial databases, namely, mutual nearest neighbor (MNN) search.  ...  Here, p 2 , p 4 , and p 5 will be out of the consideration in the subsequent assignment as they are all linked to two other branches, and the only left branch is p 1 .  ...  Suppose that we employ conventional k (P2) nearest neighbor (kNN) search, and process the branches in the order of p 1 , p 2 , p 3 , p 4 , p 5 , p 6 .  ... 
doi:10.1016/j.datak.2009.04.004 fatcat:upbbmffz4rhcdl5u45y3zx6gne

Discovering Attractive Products based on Influence Sets [article]

Anastasios Arvanitis, Antonios Deligiannakis
2011 arXiv   pre-print
In this work we develop novel algorithms for two important classes of queries involving customer preferences. We first propose a novel algorithm, termed as RSA, for answering reverse skyline queries.  ...  In this type of queries, given a set of existing product specifications P, a set of customer preferences C and a set of new candidate products Q, the k-MAC query returns the set of k candidate products  ...  The corresponding definitions are presented in appropriate areas of the text. A. Single Point Reverse Skylines Consider two sets of points, denoted as P and C, in the same D-dimensional space.  ... 
arXiv:1107.4924v1 fatcat:f2nj6zpvmrfdhjtngurkj3uune

Reverse nearest neighbor heat maps: A tool for influence exploration

Yu Sun, Rui Zhang, Andy Yuan Xue, Jianzhong Qi, Xiaoyong Du
2016 2016 IEEE 32nd International Conference on Data Engineering (ICDE)  
We study the problem of constructing a reverse nearest neighbor (RNN) heat map by finding the RNN set of every point in a two-dimensional space.  ...  The heat map provides a global view on the influence distribution in the space, and hence supports exploratory analyses in many applications such as marketing and resource management.  ...  For instance, Lu et al. [13] investigate reverse spatial and textual nearest neighbor queries, in which both location and textual descriptions are considered in the distance metric.  ... 
doi:10.1109/icde.2016.7498305 dblp:conf/icde/SunZXQD16 fatcat:w3e6dg3ewjhfjbqx4rr6piguu4

Finding Top $k$ Most Influential Spatial Facilities over Uncertain Objects

Liming Zhan, Ying Zhang, Wenjie Zhang, Xuemin Lin
2015 IEEE Transactions on Knowledge and Data Engineering  
the performance of the algorithms in terms of CPU and I/O costs.  ...  By utilizing two uncertain object indexing techniques, R-tree and U-Quadtree, effective and efficient algorithms are proposed following the filtering and verification paradigm, which significantly improves  ...  ACKNOWLEDGMENTS Ying Zhang is supported by ARC DE140100679 and DP130103245. Wenjie Zhang is supported by ARC DE120102144, DP120104168, ARC DP150103071 and DP150102728.  ... 
doi:10.1109/tkde.2015.2457899 fatcat:kvmetxxqovddphaainkwciimuy
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