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    <p>I'd say that's a pretty good solution you have so far. </p> <p>There is a few optimizations I see though. Here's my variation:</p> <pre><code>% INITIALIZE NN = 9; L = rand(1,NN-1); while numel(L) ~= NN; L = unique( randi(100,1,NN) ); end % Some bogus constraints constraints = [... L(1) L(2) L(3) L(6) L(3) L(5) L(8) L(4)]; % METHOD 0 (your original method) tic orderings = perms(L); p = size(orderings,1); c = size(constraints,1); toKeep = true(p,1); for perm = 1:p for constr = 1:c idxA = find(orderings(perm,:) == constraints(constr,1)); idxB = find(orderings(perm,:) == constraints(constr,2)); if idxA &gt; idxB toKeep(perm) = false; end end end orderings0 = orderings(toKeep,:); toc % METHOD 1 (your original, plus a few optimizations) tic orderings = perms(L); p = size(orderings,1); c = size(constraints,1); toKeep = true(p,1); for perm = 1:p for constr = 1:c % break on first condition breached if toKeep(perm) % find only *first* entry toKeep(perm) = ... find(orderings(perm,:) == constraints(constr,1), 1) &lt; ... find(orderings(perm,:) == constraints(constr,2), 1); else break end end end orderings1 = orderings(toKeep,:); toc % METHOD 2 tic orderings = perms(L); p = size(orderings,1); c = size(constraints,1); toKeep = true(p,1); for constr = 1:c % break on first condition breached1 if any(toKeep) % Vectorized search for constraint values [i1, j1] = find(orderings == constraints(constr,1)); [i2, j2] = find(orderings == constraints(constr,2)); % sort by rows [i1, j1i] = sort(i1); [i2, j2i] = sort(i2); % Check if columns meet condition toKeep = toKeep &amp; j1(j1i) &lt; j2(j2i); else break end end orderings2 = orderings(toKeep,:); toc % Check for equality all(orderings2(:) == orderings1(:)) </code></pre> <p>Results: </p> <pre><code>Elapsed time is 17.911469 seconds. % your method Elapsed time is 10.477549 seconds. % your method + optimizations Elapsed time is 2.184242 seconds. % vectorized outer loop ans = 1 ans = 1 </code></pre> <p>The whole approach however has one fundamental flaw IMHO; the direct use of <code>perms</code>. This inherently poses a limitation due to memory constraints (<code>NN &lt; 10</code>, as stated in <code>help perms</code>). </p> <p>I have a strong suspicion you can get better performance, both time-wise and memory-wise, when you put together a customized <code>perms</code>. Luckily, <code>perms</code> is not built-in, so you can start by copy-pasting that code into your custom function. </p>
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    1. USRody Oldenhuis
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