Sorting some set of number
The algorithm is studied by Yijie Han in his paper [1].

There's also a relevant question on cstheory: Han's $O(n\log\log n)$ time, linear space, integer sorting algorithm.



[1] Han, Y. (2002, May). Deterministic sorting in O (n log log n) time and linear space. In Proceedings of the thiry-fourth annual ACM symposium on Theory of computing (pp. 602-608). ACM.