Where do we go from Here?

One possible attack:

• Recall: Lund and Reingold found the optimal competitiveness
  for each 3-point metric space. (Always C e / e - 1.)

• Try to find C < 2 such that there is a C-competitive order
  2 knowledge state algorithm for every 4-point metric space.
  Why? Because for an order 2 knowledge state algorithm,
  every move involves at most 4 points.

• Try to fit them together.