Synthesis : Pan's Algorithm

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Have anyone studied Pan's Algorithm previously ?

I do not understand the code inside the while loop

 

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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 **broken link removed** 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 ?