Finding a minimum Hamming distance in less than O (n ^ 2m)

Question

If you have nbinary strings, each of the lengths m, is there a faster way to determine the minimum Hamming distance between any pair than to compare all the pairs O(n^2)and for each calculate their Hamming distance?

That is, can this be done in less than O(n^2m)?

Among other things, and as indicated below, the Hamming distance is the right function of distance and therefore satisfies the triangle inequality, which makes me feel that there needs to be a faster solution.

Answer 1

Locality Sensitive Hashing, , , . :

LSH , "" ( , ).

, LSH , . , LSH / LSH ( ). , () . (, LSH, , n^2.)

, , ( 2-3 ). / , ; LSH ( ) .