Algorithms with O(n/log(n)) complexity

问题

Are there any famous algorithms with this complexity?

I was thinking maybe a skip list where levels of the nodes are not determined by the number of tails coin tosses, but instead are use a number generated randomly (with uniform distribution) from the (1,log(n)) period to determine the level of the node. Such a data structure would have a find(x) operation with the complexity of O(n/log(n)) (I think, at least). I was curious whether there was anything else.

回答1:

It's common to see algorithms whose runtime is of the form O(n^k / log n) or O(log n / log log n) when using the method of Four Russians to speed up an existing algorithm. The classic Four Russians speedup reduces the cost of doing a matrix/vector product on Boolean matrices from O(n²) to O(n² / log n). The standard dynamic programming algorithm for sequence alignment on two length-n strings runs in time O(n²), which can be decreased to O(n² / log n) by using a similar trick.

Similarly, the prefix parity problem - in which you need to maintain a sequence of Boolean values while supporting the "flip" and "parity of the prefix of a sequence" operations can be solved in time O(log n / log log n) by using a Four-Russians speedup. (Notice that if you express the runtime as a function of k = log n, this is O(k / log k).

来源：https://stackoverflow.com/questions/35176736/algorithms-with-on-logn-complexity