XPost: sci.op-research   
   From: rubin@msu.edu   
      
   Fabrizio Riguzzi wrote:   
   > Hello,   
   > 	I would like to know if the following problem has already been studied:   
   > I have two rulers of equal length, each cut into pieces of (typically of   
   > different length and not necessarily  in the same number for the two   
   > rulers). I would like to find a way of dividing the pieces of one ruler   
   > so that the new pieces can be combined to give the pieces of the other   
   > ruler. The division must be such that it is not dominated, i.e., no two   
   > pieces can be attached and the resulting division be still a solution of   
   > the problem. I may also want to find all the possible non dominated   
   > solutions.   
   >   
   > Is there a nmae for this problem? Is there an algorithm that solves it?   
   >   
   > Thanks,   
   > Best,   
   > Fabrizio   
   >   
      
   I've never seen this problem articulated before, so I cannot supply a   
   name.  Are pieces of the same length (from the same ruler)   
   distinguishable?  For instance, do the rulers both have a "3 cm." mark,   
   and must the piece with the 3 cm. mark from ruler A (or at least the   
   portion of it containing the mark) be used to build the piece from ruler   
   B containing the same mark?  If so, then do we have to worry about other   
   gradations?  Rulers for the English system typically use unnumbered   
   marks of different lengths to indicate halves, quarters, eighths and   
   possibly sixteenths of an inch.  Do those have to be aligned as well   
   when reconstructing the pieces of B from pieces of A?   
      
   /Paul   
      
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