Counting Inversions, Offline Orthogonal Range Counting, and Related Problems

@inproceedings{Chan2010CountingIO,
  title={Counting Inversions, Offline Orthogonal Range Counting, and Related Problems},
  author={Timothy M. Chan and Mihai Patrascu},
  booktitle={SODA},
  year={2010}
}
We give an <i>O</i>(<i>n</i> √lg <i>n</i>)-time algorithm for counting the number of inversions in a permutation on <i>n</i> elements. This improves a long-standing previous bound of <i>O</i>(<i>n</i> lg <i>n</i>/ lg lg <i>n</i>) that followed from Dietz's data structure [WADS'89], and answers a question of Andersson and Petersson [SODA'95]. As Dietz's… CONTINUE READING

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