{"title":"New upper bounds for neighbor searching","authors":"B. Chazelle , R. Cole , F.P. Preparata , C. Yap","doi":"10.1016/S0019-9958(86)80030-4","DOIUrl":null,"url":null,"abstract":"<div><p>This paper investigates the circular retrieval problem and the <em>k</em>-nearest neighbor problem, for sets of <em>n</em> points in the Euclidean plane. Two similar data structures each solve both problems. A deterministic structure uses space <em>O</em>(<em>n</em>(log <em>n</em> log log <em>n</em>)<sup>2</sup>), and a probabilistic structure uses space <em>O</em>(<em>n</em> log<sup>2</sup> <em>n</em>). For both problems, these two structures answer a query that returns <em>k</em> points in <em>O</em>(<em>k</em> + log <em>n</em>) time.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1986-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80030-4","citationCount":"19","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019995886800304","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 19
Abstract
This paper investigates the circular retrieval problem and the k-nearest neighbor problem, for sets of n points in the Euclidean plane. Two similar data structures each solve both problems. A deterministic structure uses space O(n(log n log log n)2), and a probabilistic structure uses space O(n log2n). For both problems, these two structures answer a query that returns k points in O(k + log n) time.