Multiway Cut question I am trying to understand Multiway Cut, and basically how the Multiway Cut works. I am searching google many hours to find a good example to understand. A good example that I am trying to understand is this:

http://crab.rutgers.edu/~rajivg/studentTalks/multiwayCut.pdf

What I cannot understand, and here is the point I need your help, is how did he go from slide 12 to slide 13? How the graph on slide 13 was produced? How do I choose A1*,A2*,A3* ??
The analysis of the approximation algorithm (join all min-cuts between a terminal and the contraction of the remaining terminals, excluding the heaviest cut) starts on slide 13. So there's nothing to compute, simply assume that $A^*$ is the optimal solution with cuts $A_i^*$ separating terminal $i$ from the rest of the graph. To see the argument spelled out more explicitly read e.g. chapter 4 of Vazirani's "Approximation Algorithms".