How to speed up the "unique" function when sorting out unique columns

As you can see by running the example code below, the time it takes to compute the number of unique columns quickly deteriorates with matrix size.

Others have proposed ways to write inline code in order to speed this up, but those solutions do not seem to cover column-wise (alt. row-wise) uniqueness.

Please help.

clear all, close all

n = 20; % #objects

% compute all possible combinations of 0 and 1 (#combinations = 2^n)
% 0 - object is turned off
% 1 - object is active
% furthermore, as an example the states 01 and 10 are assumed to be equivalent since order is not an issue

combs = [0 1];
for i = 2:n
    combs = combvec(combs,[0 1]);
    combsSort = sort(combs, 1); % sort columnwise
  tic
    uniqueCombs = unique(combsSort.','rows').'; % find unique columns by transposing twice
    toc
    size(uniqueCombs)
end

[FirefoxMetzger]

This entire sorting can be solved by:

result = ones(N,N);
result = fliplr(tril(result));

To suggest a better algorithm (if still needed) please be more specific about what you want. The unique() command is the most efficient way to solve a general problem. However, there is often a more efficient implementation depending on the need.