Fast stable in-place sorting withO(n) data moves

Until recently, it was not known whether it was possible to sortstably (i.e., keeping equal elements in their initial order) an array ofn elements using onlyO(n) data moves andO(1) extra space. In [13] an algorithm was given to perform this task inO(n2) comparisons in the worst case. Here, we develop a new algorithm for the problem that performs onlyO(n1+ε) comparisons (0<ε<1 is any fixed constant) in the worst case. This bound on the number of comparisons matches (asymptotically) the best known bound for the same problem with the stability constraint dropped.

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