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← 10-27 Combining Structures

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Showing Revision 1 created 10/03/2012 by Amara Bot.

  1. So what I'm now going to do is--I'm going to take the structure here, make it a bit smaller like this
  2. and take away the NP here, and we are going to reappear in a minute.
  3. What I'm now going to do is I'm going to put a bunch of these structures together.
  4. So connect this one edge, connect this one edge, and we're also going to do one here
  5. and now call this one A and this one B.
  6. Now, what you see here is that I have taken three structures like these
  7. and put them between A and B.
  8. I'm going to do this more generally now.
  9. Imagine that instead of an edge here, I could have more of these structures.
  10. I'll just write three dots here and these will represent
  11. additional copies of this structure being in between here.
  12. So in total, I will have n copies of the structure--n times this structure here appears between A and B.
  13. And now my question is, how many shortest paths between A and B
  14. can you have that visit all of the vertices here.
  15. If you have n copies of that structure, is that n², is that 2^n, or is that 2n.