title: Don't understand closest pair heuristic from "The Algorithm Design Manual "
body: <p>There is almost exactly the same <a href="https://stackoverflow.com/questions/7216755/what-is-the-meaning-of-from-distinct-vertex-chains-in-this-nearest-neighbor-al/7216814#comment15114654_7216814">question</a>. But I still don't understand, how is this heuristic working and in what sequence vertexes are passed through. Also there is a picture in a book: <img src="https://i.stack.imgur.com/IC4mH.jpg" alt="enter image description here"></p>
  
  <p>That shows comparison of nearest-neghbor heuristic and what I believe is a closest-pair heuristic. From the picture I may assume that on the top picture, 0 point was selected first, but on the bottom picture there was selected the leftmost or the rightmost one. Because there is nothing said about first point selection (also the closest-pair heuristic doesn't do any actions in that), I may assume that any algorithm results however good it is won't give you the bottom picture if it doesn't consider, what point to start with. </p>
  
  <p>For now I just want to know, what steps closest-pair heuristic makes. A picture similar to the bottom one with numbers associated with each iteration along with explanation would be appreciated.</p>
  
  <p>Here is the <a href="http://www.cs.sysu.edu.cn/~lxm/DSA/textbook/Skiena.-.TheAlgorithmDesignManual.pdf" rel="noreferrer">link</a> to the book taken from that post.</p>