{"title":"如何在历史中搜索","authors":"Bernard Chazelle","doi":"10.1016/S0019-9958(85)80045-0","DOIUrl":null,"url":null,"abstract":"<div><p>This paper considers the problem of granting a dynamic data structure the capability of remembering the situation it held at previous times. We present a new scheme for recording a history of <em>h</em> updates over an ordered set <em>S</em> of <em>n</em> objects, which allows fast neighbor computation at any time in the history. The novelty of the method is to allow the set <em>S</em> to be only partially ordered with respect to queries and the time measure to be multi-dimensional. The generality of the method makes it useful for a number of problems in 3-dimensional geometry. For example, we are able to give fast algorithms for locating a point in a 3-dimensional complex, using linear space, or for finding which of <em>n</em> given points is closest to a query plane. Using a simpler, yet conceptually similar technique, we show that with <em>O</em>(<em>n</em><sup>2</sup>) preprocessing, it is possible to determine in <em>O</em>(log<sup>2</sup> <em>n</em>) time which of <em>n</em> given points in <em>E</em><sup>3</sup> is closest to an arbitrary query point.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":"64 1","pages":"Pages 77-99"},"PeriodicalIF":0.0000,"publicationDate":"1985-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(85)80045-0","citationCount":"68","resultStr":"{\"title\":\"How to search in history\",\"authors\":\"Bernard Chazelle\",\"doi\":\"10.1016/S0019-9958(85)80045-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper considers the problem of granting a dynamic data structure the capability of remembering the situation it held at previous times. We present a new scheme for recording a history of <em>h</em> updates over an ordered set <em>S</em> of <em>n</em> objects, which allows fast neighbor computation at any time in the history. The novelty of the method is to allow the set <em>S</em> to be only partially ordered with respect to queries and the time measure to be multi-dimensional. The generality of the method makes it useful for a number of problems in 3-dimensional geometry. For example, we are able to give fast algorithms for locating a point in a 3-dimensional complex, using linear space, or for finding which of <em>n</em> given points is closest to a query plane. Using a simpler, yet conceptually similar technique, we show that with <em>O</em>(<em>n</em><sup>2</sup>) preprocessing, it is possible to determine in <em>O</em>(log<sup>2</sup> <em>n</em>) time which of <em>n</em> given points in <em>E</em><sup>3</sup> is closest to an arbitrary query point.</p></div>\",\"PeriodicalId\":38164,\"journal\":{\"name\":\"信息与控制\",\"volume\":\"64 1\",\"pages\":\"Pages 77-99\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1985-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0019-9958(85)80045-0\",\"citationCount\":\"68\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"信息与控制\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019995885800450\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019995885800450","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
This paper considers the problem of granting a dynamic data structure the capability of remembering the situation it held at previous times. We present a new scheme for recording a history of h updates over an ordered set S of n objects, which allows fast neighbor computation at any time in the history. The novelty of the method is to allow the set S to be only partially ordered with respect to queries and the time measure to be multi-dimensional. The generality of the method makes it useful for a number of problems in 3-dimensional geometry. For example, we are able to give fast algorithms for locating a point in a 3-dimensional complex, using linear space, or for finding which of n given points is closest to a query plane. Using a simpler, yet conceptually similar technique, we show that with O(n2) preprocessing, it is possible to determine in O(log2n) time which of n given points in E3 is closest to an arbitrary query point.