On adaptive integer sorting (2004)
| Venue: | In 12th Annual European Symposium on Algorithms, ESA 2004 |
| Citations: | 4 - 0 self |
BibTeX
@INPROCEEDINGS{Pagh04onadaptive,
author = {Anna Pagh and Rasmus Pagh and Mikkel Thorup},
title = {On adaptive integer sorting},
booktitle = {In 12th Annual European Symposium on Algorithms, ESA 2004},
year = {2004},
pages = {556--567},
publisher = {Springer Verlag}
}
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Abstract
Abstract. This paper considers integer sorting on a RAM. We show that adaptive sorting of a sequence with qn inversions is asymptotically equivalent to multisorting groups of at most q keys, and a total of n keys. Using the recent O(n √ log log n) expected time sorting of Han and Thorup on each set, we immediately get an adaptive expected sorting time of O(n √ log log q). Interestingly, for any positive constant ε, we show that multisorting and adaptive inversion sorting can be performed in (log n)1−ε linear time if q ≤ 2. We also show how to asymptotically improve the running time of any traditional sorting algorithm on a class of inputs much broader than those with few inversions. 1
