Synthesis : Pan's Algorithm

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) ?

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

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

1. 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 ?