Synthesis : Pan's Algorithm

[promach]

Have anyone studied Pan's Algorithm previously ?


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 ?

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

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 ?