title: Selecting subset of sequences so their sum has minimum variance?
body: <p>I have a set of N real sequences and need to pick K sequences (with no replacement) such that their sum has the minimum variance.</p>
  <p>E.g. I have N=3 real sequences of length 5:</p>
  <pre><code>x(1)=[-0.9   0.7    2.0    2.5    1.5]
  x(2)=[-1.8  -0.2    0.5   -1.3   -0.7]
  x(3)=[-1.5  -0.9    0.3    1.5    0.4]
  </code></pre>
  <p>If I need to select K=2 sequences, the variance of the sums is:</p>
  <pre><code>var(x(1)+x(2))=3.7
  var(x(1)+x(3))=6.1
  var(x(2)+x(3))=2.5
  </code></pre>
  <p>So I'd want to select sequences 2 &amp; 3.</p>
  <p>This is easy to brute force for small N, but my real application has much larger N.  For example, for N=20 and K=10, there are 184756 combinations.  Since my sequence lengths are long and computational time is critical, this is not feasible.</p>
  <p>Is there an efficient algorithm to do the selection? Or even to give an approximate solution? Or reduce the problem space to likely candidates?</p>