{"title":"几何置换的改进界","authors":"Natan Rubin, Haim Kaplan, M. Sharir","doi":"10.1137/110835918","DOIUrl":null,"url":null,"abstract":"We show that the number of geometric permutations of an arbitrary collection of $n$ pair wise disjoint convex sets in $\\mathbb{R}^d$, for $d\\geq 3$, is $O(n^{2d-3}\\log n)$, improving Wenger's 20 years old bound of $O(n^{2d-2})$.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Improved Bounds for Geometric Permutations\",\"authors\":\"Natan Rubin, Haim Kaplan, M. Sharir\",\"doi\":\"10.1137/110835918\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the number of geometric permutations of an arbitrary collection of $n$ pair wise disjoint convex sets in $\\\\mathbb{R}^d$, for $d\\\\geq 3$, is $O(n^{2d-3}\\\\log n)$, improving Wenger's 20 years old bound of $O(n^{2d-2})$.\",\"PeriodicalId\":228365,\"journal\":{\"name\":\"2010 IEEE 51st Annual Symposium on Foundations of Computer Science\",\"volume\":\"6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 IEEE 51st Annual Symposium on Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/110835918\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/110835918","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We show that the number of geometric permutations of an arbitrary collection of $n$ pair wise disjoint convex sets in $\mathbb{R}^d$, for $d\geq 3$, is $O(n^{2d-3}\log n)$, improving Wenger's 20 years old bound of $O(n^{2d-2})$.
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