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Assuming that you are working with cubic cells, you can create a vector called point2cell, such that point2cell[iPoint] gives you the indeces of the cells sharing the point iPoint. This can be done by looping over the cells vector. Take a look at the following pseudo-code:

for iCell = 1:nCell
  for iPointLoc = 1:8
     iPoint = cells[iCell][iPointLoc]
     point2cell[iPoint].insert( iCell )

Next, you can loop over the faces, take one point, take all the cells sharing that point, and looking at the matching between a face and a cell:

for iFace = 1:nFace
  for iPointLoc = 1:4
    iPoint = faces[iFace][iPointLoc]
    for iCellLoc = 1:8
       iCell = point2Cell[iPoint][iCellLoc]
       if( cells[iCell] matches faces[iFace])
         face2cell[iFace].insert( iCell ) 

The first loop is linear in the number of cells while the second is linear in the number of faces.