It should be a very easy question, but I am a little bit confused. According to party optimization post, the Maximum-weight Independent Set for trees can be found in the poly-nominal time using Dynamic Programming (the Algorithm is also explained on page 562 of the book Algorithm Design). Now, imagine that we want to trace the algorithm on a random graph like the figure below where the numbers in the balls show the weight.
I want to know, does it matter which node I am selecting as the root? Can you please guide me through the steps of this algorithm's tracing on this graph?