Thanks again Tom.   
      
   > > When a path is updated or "replaced" in this way, all of its   
   children   
   > > must also be replaced (or deleted, if this is faster).   
   >   
   > For purposes of reconstructing the best path at the end of the   
   > algorithm?   
      
   No, as you write, we can   
      
   > just store one back-pointer per node per keyset and reconstruct the   
   > path backwards from the goal.   
      
   My concern is that children of deprecated ("replaced") key/path-sets   
   might waste computation time (and memory space) by unnecessarily   
   propagating deprecated information. Even if we choose the next node to   
   expand based on the shortest distance of any path in its key/path-set,   
   we still risk propagating deprecated key/path information when the   
   deprecated key/path is not the shortest one in its key/path-set. If,   
   however, we propagate only the shortest-path element in the   
   shortest-path key/path-set, I think this is no longer a problem.   
      
   (I'd be happy to provide some examples and further discussion if this   
   is unclear.)   
      
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