The paper closes with > However, we felt that computing the determinant for all possible sub matrices is a bottleneck for this algorithm and ways should be fou

The paper closes with > However, we felt that computing the determinant for all possible sub matrices is a bottleneck for this algorithm and ways should be found to make this more efficient. That last step is obviously of exponential complexity in the parameters r and t. I wonder whether the algorithm's total run-time becomes more acceptable when that last step is replaced by a polynomial-complexity computation. To me it looks like an O(log(n)*n³) algorithm should be feasible, by replacing the submatrix-determinants with operations on determinants on large matrices that are generated in a way that ensures det=0 when any of the sub-matrices has det=0. Unfortunately I don't really understand enough about the remainder of the paper to actually see how the useful the algorithm would be with that "bottleneck" removed.