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Correlating two lists

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100150] Correlating two lists
  • From: anguzman at ing.uchile.cl
  • Date: Tue, 26 May 2009 05:11:05 -0400 (EDT)
  • References: <gv2jr1$9af$1@smc.vnet.net>

Hi all.
I have the following problem:
Two lists: "x" and "y";  and a boolean relation R[a,b] with a in x and 
b in y, and for each "a" there is at most one "b" in "y" such that 
R[xi,yj]is true.
R is also "expensive" to calculate. I would like to group each xi in 
"x" with its partner in "y" (if there is one) and create a merged list:
{{x1,y1},{x2},{x3},{x4,y4},...}
such that R[xi,yi]  is true
I'm looking for the adequate Mathematica function to do this as 
efficiently as possible. by the way, I'm using now this 
straightforward-naive approach:

merged={};
Do[Do[If[R[xi,yj],merged=Append[merged,{xi,yj}]],{yj,y}];If[MemberQ[merge[[All,1]],xi],merged=Append[merged,{xi}]],{xi,x}]

but I'm sure there must be a better one (without the Do's would be beautiful).
Any thoughts will be greatly appreciated.
Thanks in advance, and cheers for the 100.000

Atte. Andres Guzman

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