Have anyone studied Pan's Algorithm previously ?

http://people.eecs.berkeley.edu/~alanmi/publications/2005/iwls05_smr.pdf#page=3 

https://i.imgur.com/GO8s4BU.png


1.    How is Pan's algorithm being a shortest-path algorithm when clock period is computed across the critical path (longest path) ?

2.    Any idea about the modified version of Pan's algorithm described in Figure 2 on page 4 ?   

http://people.eecs.berkeley.edu/~alanmi/publications/2005/iwls05_smr.pdf#page=4


3.    How does Howard's algorithm avoids re-mapping of the non-critical nodes ?    

https://twin.sci-hub.do/5837/84bca870f4f7cc8a1ff7ea72d2d6de8e/algorithms-and-computation-2010.pdf#%5B%7B%22num%22%3A8305%2C%22gen%22%3A0%7D%2C%7B%22name%22%3A%22FitH%22%7D%2C730%5D

http://people.eecs.berkeley.edu/~alanmi/publications/2005/iwls05_smr.pdf#page=5


4.    It seems that Figures 2 and 3 of another paper : An Integrated Technology Mapping Environment resemble Pan's Algorithm ?
       Why do the paper authors state that for a given node, the fanin are known at current optimization iteration, but the fanouts are known only for the previous optimization iteration ?

https://people.eecs.berkeley.edu/~alanmi/research/iwls05/iwls05_env.pdf#page=3