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New Upper Bounds in Klee's Measure Problem (Extended Abstract)  (Make Corrections)  
Overmars measure problem RUU-CS-88-22 Rijksuniversiteit Utrecht Vakgroep informatica...
IEEE Symposium on Foundations of Computer Science



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Abstract: Abstract We give new upper bounds for the measure problem of Klee which significantly improve the previous bounds for dimensions greater than 2. We obtain an O(n d/2 log n, n logn) time-space upper bound to compute the measure of a set of n boxes in Euclidean &space. The solution requires several new ideas including application of the inclusion/exclusion principle, the concept of trellises, streaming, and a partition of d-space. (Update)

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BibTeX entry:   (Update)

@inproceedings{ overmars88new,
    author = "Mark H. Overmars and Chee-Keng Yap",
    title = "New upper bounds in Klee's measure problem (extended abstract)",
    booktitle = "{IEEE} Symposium on Foundations of Computer Science",
    pages = "550-556",
    year = "1988",
    url = "citeseer.ist.psu.edu/article/overmars88new.html" }
Citations (may not include all citations):
508   Computational Geometry (context) - Preparata - 1985
346   Multidimensional binary search trees used for associated sea.. (context) - Bentley - 1975
37   Algorithms for Klee's rectangle problem (context) - Bentley - 1977
29   Batched dynamic solutions to decomposable searching problems (context) - Edelsbrunner - 1985
27   Partition trees for triangle counting and other range search.. (context) - Welzl - 1988
21   Polygon retrieval (context) - Willard - 1982
2   be computed in less than O (context) - Klee, Can - 1977
2   The measure problem for rectangular ranges in d-space (context) - van Leeuwen - 1980
1   The complexity of computing the measure of U[ai (context) - Fredman - 1978

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