title: A greedy or dynamic algorithm to subset selection
body: <p>I have a simple algorithmic question. I would be grateful if you could help me.</p>
  
  <p>We have some 2 dimensional points. A positive weight is associated to them (a sample problem is attached). We want to select a subset of them which maximizes the weights and neither of two selected points overlap each other (for example, in the attached file, we cannot select both A and C because they are in the same row, and in the same way we cannot select both A and B, because they are in the same column.) If there is any greedy (or dynamic) approach I can use. I'm aware of non-overlapping interval selection algorithm, but I cannot use it here, because my problem is 2 dimensional.</p>
  
  <p>Any reference or note is appreciated.</p>
  
  <p>Regards</p>
  
  <p>Attachment:
  A simple sample of the problem:</p>
  
  <pre>   
     A (30$) --------  B (10$)
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     C (8$)
  
  </pre>