[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657639-105":59,"doc-detail-657639-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","vor-tree-r-trees-with-voronoi-diagrams-for-efficient-processing-of-spatial-nearest-neighbor-queries","VoR-Tree: R-trees with Voronoi Diagrams for Efficient Processing of Spatial Nearest Neighbor Queries","","A spatial nearest neighbor query framework often relies on R-trees in two phases: logarithmic-time discovery of a local neighborhood and subsequent investigation of intersecting nodes, which can cause excessive, unnecessary traversal. Recent work shows Voronoi diagrams efficiently explore the search region but reach it slowly without an access method. VoR-Tree integrates Voronoi tiling with coarse R-tree rectangles to reach the region quickly and enumerate results, yielding improved I/O complexity across multiple NN variants.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/vor-tree-r-trees-with-voronoi-diagrams-for-efficient-processing-of-spatial-nearest-neighbor-queries/657639/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/vor-tree-r-trees-with-voronoi-diagrams-for-efficient-processing-of-spatial-nearest-neighbor-queries/657639.png","ImageObject",300,407,{"name":92,"@type":93},"BAd apple","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does VoR-Tree address in nearest neighbor queries?","Question",{"text":112,"@type":113},"R-tree based methods efficiently reach a neighborhood, but then examine many nodes that contain few or none of the true results. VoR-Tree reduces unnecessary investigation while still enabling fast access to the search region.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does VoR-Tree combine R-trees and Voronoi diagrams?",{"text":117,"@type":113},"VoR-Tree uses R-tree coarse rectangle nodes to reach the search region in logarithmic time, then uses Voronoi diagram fine polygons to tile/cover the region and find the result set.",{"name":119,"@type":110,"acceptedAnswer":120},"What advantage does VoR-Tree provide over best competitors?",{"text":121,"@type":113},"The proposed algorithms for various nearest neighbor query types achieve better I/O complexity than their best existing competitors.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657639,1793073031,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":41},19241458193282,"https://us-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","VoR-Tree: R-trees with Voronoi Diagrams for Efficient Processing of Spatial Nearest Neighbor Queries􀀃  \nMehdi Sharifzadeh  \ny  \nGoogle [mehdish@google.com](mehdish@google.com)  \nCyrus Shahabi  \nUniversity of Southern California  \n[shahabi@usc.edu](shahabi@usc.edu)  \nABSTRACT  \nA very important class of spatial queries consists of nearestneighbor (NN) query and its variations. Many studies in the past decade utilize R-trees as their underlying index structures to address NN queries e􀀎ciently. The general approach is to use R-tree in two phases. First, R-tree's hierarchical structure is used to quickly arrive to the neighborhood of the result set. Second, the R-tree nodes intersecting with the local neighborhood (Search Region) of an initial answer are investigated to 􀀌nd all the members of the result set. While R-trees are very e􀀎cient for the 􀀌rst phase, they usually result in the unnecessary investigation of many nodes that none or only a small subset of their including points belongs to the actual result set.  \nOn the other hand, several recent studies showed that the Voronoi diagrams are extremely e􀀎cient in exploring an NN search region, while due to lack of an e􀀎cient access method, their arrival to this region is slow. In this paper, we propose a new index structure, termed VoR-Tree that incorporates Voronoi diagrams into R-tree, bene􀀌ting from the best of both worlds. The coarse granule rectangle nodes of R-tree enable us to get to the search region in logarithmic time while the 􀀌ne granule polygons of Voronoi diagram allow us to e􀀎ciently tile or cover the region and 􀀌nd the result. Utilizing VoR-Tree, we propose e􀀎cient algorithms for various Nearest Neighbor queries, and show that our algorithms have better I/O complexity than their best competitors.  \n1. INTRODUCTION  \n􀀃 This research has been funded in part by NSF grants IIS- 0238560 (PECASE), IIS-0534761, and CNS-0831505 (CyberTrust), the NSF Center for Embedded Networked Sensing (CCR-0120778) and in part from the METRANS Transportation Center, under grants from USDOT and Caltrans. Any opinions, 􀀌ndings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily re􀀍ect the views of the National Science Foundation.  \ny The work was completed when the author was studying PhD at USC's InfoLab.  \nPermission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Articles from this volume were presented at The 36th International Conference on Very Large Data Bases, September 13-17, 2010, Singapore.  \nProceedings of the VLDB Endowment, Vol. 3, No. 1  \nCopyright 2010 VLDB Endowment 2150-8097/10/09 ... $ 10.00.  \nAn important class of queries, especially in the geospatial domain, is the class of nearest neighbor (NN) queries. These queries search for data objects that minimize a distancebased function with reference to one or more query objects. Examples are k Nearest Neighbor (kNN) [13, 5, 7], Reverse k Nearest Neighbor (RkNN) [8, 15, 16], k Aggregate Nearest Neighbor (kANN) [12] and skyline queries [1, 11, 14] . The applications of NN queries are numerous in geospatial decision making, location-based services, and sensor networks.  \nThe introduction of R-trees [3](and their extensions) for indexing multi-dimensional data marked a new era in developing novel R-tree-based algorithms for various forms of Nearest Neighbor (NN) queries. These algorithms utilize the simple rectangular grouping principle used by Rtree that represents close data points with their Minimum Bounding Rectangle (MBR) . They generally use R-tree in two phases. In the 􀀌rst phase, starting from the root node, they ite","cbCailXvBMipSaxf","https://ap.wps.com/l/cbCailXvBMipSaxf","pdf",1166583,12,"English","# Abstract\n# Introduction","[{\"question\":\"What problem does VoR-Tree address in nearest neighbor queries?\",\"answer\":\"R-tree based methods efficiently reach a neighborhood, but then examine many nodes that contain few or none of the true results. VoR-Tree reduces unnecessary investigation while still enabling fast access to the search region.\"},{\"question\":\"How does VoR-Tree combine R-trees and Voronoi diagrams?\",\"answer\":\"VoR-Tree uses R-tree coarse rectangle nodes to reach the search region in logarithmic time, then uses Voronoi diagram fine polygons to tile/cover the region and find the result set.\"},{\"question\":\"What advantage does VoR-Tree provide over best competitors?\",\"answer\":\"The proposed algorithms for various nearest neighbor query types achieve better I/O complexity than their best existing competitors.\"}]","VoR-Tree: R-trees with Voronoi Diagrams for Efficient Processing of Spatial Nearest Neighbor Queries | PDF",1792985743]