MFs_merge potential problem

[raovgarimella]

Here is a 1D cartoon of a potential problem that might arise during parallel merge

                      Proc 1                             Proc 2
                 O1           G2                     G1           O2
(nothing here)  x========x------------x          x------------x========x   (nothing here)   
                o2       o1          g3          g2          g1        o3

The upper case letters are cells, the lower case letters are "faces". O or o means owned and G or g means ghost entity.
Say we are deleting O1 and merging o1 and o2. Then o1 will be an owned "face" with no owned "cells" connected. If we delete O2 and merge g1 and o3 while keeping o3 we will face a similar problem. However, if we delete o3, then g3 will not have a master entity.

There is no real way to do this correctly other than to do the modification on one processor and transmit the info to the other. And even then we may have an issue. What do we do?