{"title":"Klee测度问题的新上界","authors":"M. Overmars, C. Yap","doi":"10.1109/SFCS.1988.21971","DOIUrl":null,"url":null,"abstract":"New upper bounds are given for the measure problem of V. Klee (1977) that significantly improve the previous bounds for dimensions greater than 2. An O(n/sup d/2/ log n, n) time-space upper bound to compute the measure of a set of n boxes in Euclidean d-space is obtained. The solution requires several novel ideas including application of the inclusion/exclusion principle, the concept of trellises, streaming, and a partition of d-space.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"161","resultStr":"{\"title\":\"New upper bounds in Klee's measure problem\",\"authors\":\"M. Overmars, C. Yap\",\"doi\":\"10.1109/SFCS.1988.21971\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"New upper bounds are given for the measure problem of V. Klee (1977) that significantly improve the previous bounds for dimensions greater than 2. An O(n/sup d/2/ log n, n) time-space upper bound to compute the measure of a set of n boxes in Euclidean d-space is obtained. The solution requires several novel ideas including application of the inclusion/exclusion principle, the concept of trellises, streaming, and a partition of d-space.<<ETX>>\",\"PeriodicalId\":113255,\"journal\":{\"name\":\"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science\",\"volume\":\"31 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"161\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1988.21971\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1988.21971","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 161
摘要
对于V. Klee(1977)的测度问题，给出了新的上界，显著改进了先前的大于2维的上界。得到了一个O(n/sup / d/2/ log n, n)的时空上界，用于计算欧几里得d空间中n个盒子的测度。这个解决方案需要一些新颖的想法，包括包含/排除原则的应用、网格的概念、流和d空间的划分
New upper bounds are given for the measure problem of V. Klee (1977) that significantly improve the previous bounds for dimensions greater than 2. An O(n/sup d/2/ log n, n) time-space upper bound to compute the measure of a set of n boxes in Euclidean d-space is obtained. The solution requires several novel ideas including application of the inclusion/exclusion principle, the concept of trellises, streaming, and a partition of d-space.<>
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