loop over one-bits of an integer

If you need to have a loop iterated as many times as there are 1-bits in an integer v it is better to write for (;v;v &= v-1) than for (i = popcnt(v); i>0; i--) because the former has O(popcnt(v)) compexity against the latter's O(width(v)).

a submatrix problem

This problem is said to be proposed by Knuth: given an m*n (m<n) maxtix A of rank m find its m*m submatrix B such that all elements of of B^{-1}A have absolute value at most one.

Source: Local Search in Combinatorial Optimization E. Aarts, K. Lenstra, chapter 2