On Adaptive Integer Sorting

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 linear time if q ≤ 2(log n)1−ε . 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.

• Type: Conference
• Year: 2004
• Where: ESA
• Authors: Anna Pagh, Rasmus Pagh, Mikkel Thorup
• Keywords: Adaptive Sorting, ESA 2004, Paper Considers Integer, Sorting