RAM上的动态正交范围搜索，重访

Q4 Mathematics

International Journal of Computational Geometry & Applications Pub Date : 2017-06-01 DOI:10.4230/LIPIcs.SoCG.2017.28

Timothy M. Chan, Konstantinos Tsakalidis

{"title":"RAM上的动态正交范围搜索，重访","authors":"Timothy M. Chan, Konstantinos Tsakalidis","doi":"10.4230/LIPIcs.SoCG.2017.28","DOIUrl":null,"url":null,"abstract":"© Timothy M. Chan and Konstantinos Tsakalidis. We study a longstanding problem in computational geometry: 2-d dynamic orthogonal range reporting. We present a new data structure achieving O(log n/log log n+k) optimal query time and O(log2/3+o(1)n) update time (amortized) in the word RAM model, where n is the number of data points and k is the output size. This is the first improvement in over 10 years of Mortensen's previous result [SIAM J. Comput., 2006], which has O (log7/8/ϵn) update time for an arbitrarily small constant ϵ. In the case of 3-sided queries, our update time reduces to O (log1/2+ϵn), improving Wilkinson's previous bound [ESA 2014] of O(log2/3+ϵ).","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"39 1","pages":"45-66"},"PeriodicalIF":0.0000,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":"{\"title\":\"Dynamic Orthogonal Range Searching on the RAM, Revisited\",\"authors\":\"Timothy M. Chan, Konstantinos Tsakalidis\",\"doi\":\"10.4230/LIPIcs.SoCG.2017.28\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"© Timothy M. Chan and Konstantinos Tsakalidis. We study a longstanding problem in computational geometry: 2-d dynamic orthogonal range reporting. We present a new data structure achieving O(log n/log log n+k) optimal query time and O(log2/3+o(1)n) update time (amortized) in the word RAM model, where n is the number of data points and k is the output size. This is the first improvement in over 10 years of Mortensen's previous result [SIAM J. Comput., 2006], which has O (log7/8/ϵn) update time for an arbitrarily small constant ϵ. In the case of 3-sided queries, our update time reduces to O (log1/2+ϵn), improving Wilkinson's previous bound [ESA 2014] of O(log2/3+ϵ).\",\"PeriodicalId\":54969,\"journal\":{\"name\":\"International Journal of Computational Geometry & Applications\",\"volume\":\"39 1\",\"pages\":\"45-66\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Computational Geometry & Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.SoCG.2017.28\",\"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":"International Journal of Computational Geometry & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.SoCG.2017.28","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: 20

摘要

©Timothy M. Chan和Konstantinos Tsakalidis。我们研究了计算几何中一个长期存在的问题:二维动态正交范围报告。我们提出了一种新的数据结构，在word RAM模型中实现了O(log n/log log n+k)最优查询时间和O(log2/3+ O(1)n)更新时间(平摊)，其中n是数据点的数量，k是输出大小。这是Mortensen之前的结果10多年来的第一次改进[SIAM J. Comput]。， 2006]，它有O (log7/8/ϵn)更新时间为任意小的常数λ。在三面查询的情况下，我们的更新时间减少到O(log1/2+ϵn)，改进了威尔金森之前的界限[ESA 2014] O(log2/3+ λ)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Dynamic Orthogonal Range Searching on the RAM, Revisited

© Timothy M. Chan and Konstantinos Tsakalidis. We study a longstanding problem in computational geometry: 2-d dynamic orthogonal range reporting. We present a new data structure achieving O(log n/log log n+k) optimal query time and O(log2/3+o(1)n) update time (amortized) in the word RAM model, where n is the number of data points and k is the output size. This is the first improvement in over 10 years of Mortensen's previous result [SIAM J. Comput., 2006], which has O (log7/8/ϵn) update time for an arbitrarily small constant ϵ. In the case of 3-sided queries, our update time reduces to O (log1/2+ϵn), improving Wilkinson's previous bound [ESA 2014] of O(log2/3+ϵ).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

International Journal of Computational Geometry & Applications 数学-计算机：理论方法

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The International Journal of Computational Geometry & Applications (IJCGA) is a quarterly journal devoted to the field of computational geometry within the framework of design and analysis of algorithms. Emphasis is placed on the computational aspects of geometric problems that arise in various fields of science and engineering including computer-aided geometry design (CAGD), computer graphics, constructive solid geometry (CSG), operations research, pattern recognition, robotics, solid modelling, VLSI routing/layout, and others. Research contributions ranging from theoretical results in algorithm design — sequential or parallel, probabilistic or randomized algorithms — to applications in the above-mentioned areas are welcome. Research findings or experiences in the implementations of geometric algorithms, such as numerical stability, and papers with a geometric flavour related to algorithms or the application areas of computational geometry are also welcome.