title: Proving approximation for TSP-metric
body: <p>I got stuck with the following question:</p>
  
  <p>Consider the following heuristic: Start with a tour containing only one vertex. At each step, find the vertex outside the tour with the lesser distance to some vertex of the tour. Let v be the outter vertex and u be the inner vertex. Add v right after u in the tour. Suppose that your edges follow the triangle distance property. How can we show that this heuristic is a 2-approximation for the TSP-metric problem?</p>
  
  <p>Does anyone know how to start that?</p>
  
  <p>Thanks in advance</p>