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- W4244525603 abstract "We introduce a process called geometric sorting, which can be applied to an arbitrary configuration of points in d space, and which encodes in compact form the order properties of the configuration, just as the arrangement of a set of numbers in size place encodes its order properties. We give an algorithm for carrying out this sorting procedure in time $O(n^d log n)$, which generalizes the optimum sorting time of $O(nlog n)$ for the linear case; In addition, we give an efficient algorithm for determining whether two randomly numbered configurations in $mathbb{R}^d $ have the same order type, using a distinguished family of orderings of each. Finally, we indicate how this new concept of sorting can be applied to problems in pattern recognition, stereochemistry, and cluster analysis." @default.
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- W4244525603 date "1983-08-01" @default.
- W4244525603 modified "2023-09-27" @default.
- W4244525603 title "Multidimensional Sorting" @default.
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- W4244525603 doi "https://doi.org/10.1137/0212032" @default.
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